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University of Massachusetts Amherst
Mathematics and Statistics Department Faculty Publication Series
- Discipline
- Keyword
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- Automorphic forms (1)
- Bifurcation (1)
- Blume-Capel model (1)
- Bose-Einstein condensation (1)
- Bound state (1)
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- Cohomology of arithmetic groups (1)
- Dark solitions (1)
- Defocusing photonic lattices (1)
- Dipoles (1)
- Discrete nonlinear Schrodinger equation (1)
- Discrete vortices (1)
- Eigenvalues (1)
- Eisenstein cohomology (1)
- Existence and stability (1)
- First-order phase transition (1)
- Ginzburg-Landau phenomenology (1)
- Gross-Pitaevskii (1)
- Gross-Pitaevskii equation (1)
- Hecke operators (1)
- Lyapunov-schmidt reductions (1)
- Nonlinear Schrodinger (1)
- Persistence and stability (1)
- Quadrupoles (1)
- Scaling theory (1)
- Second-order phase transition (1)
- Siegel modular forms (1)
- Soliton (1)
- Solitons (1)
- Stability (1)
- Symbolic computations (1)
Articles 1 - 30 of 41
Full-Text Articles in Physical Sciences and Mathematics
Semiinfiniate Flags. Ii. Local And Global Intersection Cohomology Of Quasimaps' Spaces, Boris Feigin, Michael Finkelberg, Alexander Kuznetsov, Ivan Mirkoviæ
Semiinfiniate Flags. Ii. Local And Global Intersection Cohomology Of Quasimaps' Spaces, Boris Feigin, Michael Finkelberg, Alexander Kuznetsov, Ivan Mirkoviæ
Mathematics and Statistics Department Faculty Publication Series
No abstract provided.
Local Torsion On Elliptic Curves And The Deformation Theory Of Galois Representations, C David, T Weston
Local Torsion On Elliptic Curves And The Deformation Theory Of Galois Representations, C David, T Weston
Mathematics and Statistics Department Faculty Publication Series
No abstract provided.
Dipole And Quadrupole Solitons In Optically-Induced Two-Dimensional Defocusing Photonic Lattices, H Susanto, Kjh Law, Pg Kevrekidis, L Tang, C Lou, X Wang, Z Chen
Dipole And Quadrupole Solitons In Optically-Induced Two-Dimensional Defocusing Photonic Lattices, H Susanto, Kjh Law, Pg Kevrekidis, L Tang, C Lou, X Wang, Z Chen
Mathematics and Statistics Department Faculty Publication Series
We demonstrate a possibility to generate localized states in effectively one-dimensional Bose-Einstein condensates with a negative scattering length in the form of a dark soliton in the presence of an optical lattice (OL) and/or a parabolic magnetic trap. We connect such structures with twisted localized modes (TLMs) that were previously found in the discrete nonlinear Schrödinger equation. Families of these structures are found as functions of the OL strength, tightness of the magnetic trap and chemical potential, and their stability regions are identified. Stable bound states of two TLMs are also found. In the case when the TLMs are unstable, …
Dark Solitons In External Potentials, De Pelinovsky, Pg Kevrekidis
Dark Solitons In External Potentials, De Pelinovsky, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We consider the persistence and stability of dark solitons in the Gross–Pitaevskii (GP) equation with a small decaying potential. We show that families of black solitons with zero speed originate from extremal points of an appropriately defined effective potential and persist for sufficiently small strength of the potential. We prove that families at the maximum points are generally unstable with exactly one real positive eigenvalue, while families at the minimum points are generally unstable with exactly two complex-conjugated eigenvalues with positive real part. This mechanism of destabilization of the black soliton is confirmed in numerical approximations of eigenvalues of the …
Rabi Switch Of Condensate Wave Functions In A Multicomponent Bose Gas, He Nistazakis, Z Rapti, Dj Frantzeskakis, Pg Kevrekidis, P Sodano, A Trombettoni
Rabi Switch Of Condensate Wave Functions In A Multicomponent Bose Gas, He Nistazakis, Z Rapti, Dj Frantzeskakis, Pg Kevrekidis, P Sodano, A Trombettoni
Mathematics and Statistics Department Faculty Publication Series
Using a time-dependent linear (Rabi) coupling between the components of a weakly interacting multicomponent Bose-Einstein condensate (BEC), we propose a protocol for transferring the wave function of one component to the other. This “Rabi switch” can be generated in a binary BEC mixture by an electromagnetic field between the two components, typically two hyperfine states. When the wave function to be transferred is, at a given time, a stationary state of the multicomponent Hamiltonian, then, after a time delay (depending on the Rabi frequency), it is possible to have the same wave function on the other condensate. The Rabi switch …
Bright-Dark Soliton Complexes In Spinor Bose-Einstein Condensates, He Nistazakis, Dj Frantzeskakis, Pg Kevrekidis, Ba Malomed, R Carretero-Gonzalez
Bright-Dark Soliton Complexes In Spinor Bose-Einstein Condensates, He Nistazakis, Dj Frantzeskakis, Pg Kevrekidis, Ba Malomed, R Carretero-Gonzalez
Mathematics and Statistics Department Faculty Publication Series
We consider vector solitons of mixed bright-dark types in quasi-one-dimensional spinor (F=1) Bose-Einstein condensates. Using a multiscale expansion technique, we reduce the corresponding nonintegrable system of three coupled Gross-Pitaevskii equations (GPEs) to an integrable Yajima-Oikawa system. In this way, we obtain approximate solutions for small-amplitude vector solitons of dark-dark-bright and bright-bright-dark types, in terms of the mF=+1,−1,0 spinor components, respectively. By means of numerical simulations of the full GPE system, we demonstrate that these states indeed feature soliton properties, i.e., they propagate undistorted and undergo quasielastic collisions. It is also shown that in the presence of a parabolic trap the …
Radially Symmetric Nonlinear States Of Harmonically Trapped Bose-Einstein Condensates, G Herring, Ld Carr, R Carretero-Gonzalez, Pg Kevrekidis, Dj Frantzeskakis
Radially Symmetric Nonlinear States Of Harmonically Trapped Bose-Einstein Condensates, G Herring, Ld Carr, R Carretero-Gonzalez, Pg Kevrekidis, Dj Frantzeskakis
Mathematics and Statistics Department Faculty Publication Series
Starting from the spectrum of the radially symmetric quantum harmonic oscillator in two dimensions, we create a large set of nonlinear solutions. The relevant three principal branches, with nr=0,1, and 2 radial nodes, respectively, are systematically continued as a function of the chemical potential and their linear stability is analyzed in detail, in the absence as well as in the presence of topological charge m, i.e., vorticity. It is found that for repulsive interatomic interactions only the ground state is linearly stable throughout the parameter range examined. Furthermore, this is true for topological charges m=0 or 1; solutions with higher …
Lyapunov-Schmidt Reduction Algorithm For Three-Dimensional Discrete Vortices, M Lukas, D Pelinovsky, Pg Kevrekidis
Lyapunov-Schmidt Reduction Algorithm For Three-Dimensional Discrete Vortices, M Lukas, D Pelinovsky, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We address the persistence and stability of three-dimensional vortex configurations in the discrete nonlinear Schrödinger equation and develop a symbolic package based on Wolfram’s MATHEMATICA for computations of the Lyapunov–Schmidt reduction method. The Lyapunov–Schmidt reduction method is a theoretical tool which enables us to study continuations and terminations of the discrete vortices for small coupling between lattice nodes as well as the spectral stability of the persistent configurations. The method was developed earlier in the context of the two-dimensional lattice and applied to the onsite and offsite configurations (called the vortex cross and the vortex cell) by using semianalytical computations …
Asymptotic Behavior Of The Magnetization Near Critical And Tricritical Points Via Ginzburg-Landau Polynomials, Rs Ellis, J Machta, Pth Otto
Asymptotic Behavior Of The Magnetization Near Critical And Tricritical Points Via Ginzburg-Landau Polynomials, Rs Ellis, J Machta, Pth Otto
Mathematics and Statistics Department Faculty Publication Series
The purpose of this paper is to prove connections among the asymptotic behavior of the magnetization, the structure of the phase transitions, and a class of polynomials that we call the Ginzburg–Landau polynomials. The model under study is a mean-field version of a lattice spin model due to Blume and Capel. It is defined by a probability distribution that depends on the parameters β and K, which represent, respectively, the inverse temperature and the interaction strength. Our main focus is on the asymptotic behavior of the magnetization m(β n ,K n ) for appropriate sequences ( …
Cohomology Of Congruence Subgroups Of Sl(4, Z) Ii, A Ash, Pe Gunnells, M Mcconnell
Cohomology Of Congruence Subgroups Of Sl(4, Z) Ii, A Ash, Pe Gunnells, M Mcconnell
Mathematics and Statistics Department Faculty Publication Series
In a previous paper [3] we computed cohomology groups H5(..0(N),C), where ..0(N) is a certain congruence subgroup of SL(4,Z), for a range of levels N. In this note we update this earlier work by extending the range of levels and describe cuspidal cohomology classes and additional boundary phenomena found since the publication of [3]. The cuspidal cohomology classes in this paper are the first cuspforms for GL(4) concretely constructed in terms of Betti cohomology.
Quiver Varieties And Beilinson-Drinfeld Grassmannians Of Type A, I Mirkovic, M Vybornov
Quiver Varieties And Beilinson-Drinfeld Grassmannians Of Type A, I Mirkovic, M Vybornov
Mathematics and Statistics Department Faculty Publication Series
No abstract provided.
Approximation Of Solitons In The Discrete Nls Equation, J Cuevas, G James, Pg Kevrekidis, Ba Malomed, B Sanchez-Rey
Approximation Of Solitons In The Discrete Nls Equation, J Cuevas, G James, Pg Kevrekidis, Ba Malomed, B Sanchez-Rey
Mathematics and Statistics Department Faculty Publication Series
We study four different approximations for finding the profile of discrete solitons in the one- dimensional Discrete Nonlinear Schrödinger (DNLS) Equation. Three of them are discrete approximations (namely, a variational approach, an approximation to homoclinic orbits and a Green-function approach), and the other one is a quasi-continuum approximation. All the results are compared with numerical computations.
Two-Component Nonlinear Schrodinger Models With A Double-Well Potential, C Wang, Pg Kevrekidis, N Whitaker, Ba Malomed
Two-Component Nonlinear Schrodinger Models With A Double-Well Potential, C Wang, Pg Kevrekidis, N Whitaker, Ba Malomed
Mathematics and Statistics Department Faculty Publication Series
We introduce a model motivated by studies of Bose–Einstein condensates (BECs) trapped in double-well potentials. We assume that a mixture of two hyperfine states of the same atomic species is loaded in such a trap. The analysis is focused on symmetry-breaking bifurcations in the system, starting at the linear limit and gradually increasing the nonlinearity. Depending on values of the chemical potentials of the two species, we find numerous states, as well as symmetry-breaking bifurcations, in addition to those known in the single-component setting. These branches, which include all relevant stationary solutions of the problem, are predicted analytically by means …
Radiationless Energy Exchange In Three-Soliton Collisions, Sv Dmitriev, Pg Kevrekidis, Ys Kivshar
Radiationless Energy Exchange In Three-Soliton Collisions, Sv Dmitriev, Pg Kevrekidis, Ys Kivshar
Mathematics and Statistics Department Faculty Publication Series
We revisit the problem of the three-soliton collisions in the weakly perturbed sine-Gordon equation and develop an effective three-particle model allowing us to explain many interesting features observed in numerical simulations of the soliton collisions. In particular, we explain why collisions between two kinks and one antikink are observed to be practically elastic or strongly inelastic depending on relative initial positions of the kinks. The fact that the three-soliton collisions become more elastic with an increase in the collision velocity also becomes clear in the framework of the three-particle model. The three-particle model does not involve internal modes of the …
Stability Of Quantized Vortices In A Bose-Einstein Condensate Confined In An Optical Lattice, Kjh Law, L Qiao, Pg Kevrekidis, Ig Kevrekidis
Stability Of Quantized Vortices In A Bose-Einstein Condensate Confined In An Optical Lattice, Kjh Law, L Qiao, Pg Kevrekidis, Ig Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We investigate the existence and especially the linear stability of single- and multiple-charge quantized vortex states of nonlinear Schrödinger equations in the presence of a periodic and a parabolic potential in two spatial dimensions. The study is motivated by an examination of pancake-shaped Bose-Einstein condensates in the presence of magnetic and optical confinement. A two-parameter space of the condensate’s chemical potential versus the periodic potential’s strength is scanned for both single- and double-quantized vortex states located at a local minimum or a local maximum of the lattice. Triple-charged vortices are also briefly discussed. Single-charged vortices are found to be stable …
Stability Of Discrete Dark Solitons In Nonlinear Schrodinger Lattices, De Pelinovsky, Pg Kevrekidis
Stability Of Discrete Dark Solitons In Nonlinear Schrodinger Lattices, De Pelinovsky, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
This is the pre-published version harvested from arXiv. The published version is located at http://pre.aps.org/abstract/PRE/v74/i6/e067601
Matter-Wave Solitons With A Periodic, Piecewise-Constant Scattering Length, As Rodrigues, Pg Kevrekidis, Ma Porter, Dj Frantzeskakis, P Schmelcher, Ar Bishop
Matter-Wave Solitons With A Periodic, Piecewise-Constant Scattering Length, As Rodrigues, Pg Kevrekidis, Ma Porter, Dj Frantzeskakis, P Schmelcher, Ar Bishop
Mathematics and Statistics Department Faculty Publication Series
Motivated by recent proposals of “collisionally inhomogeneous” Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we study the existence and stability properties of bright and dark matter-wave solitons of a BEC characterized by a periodic, piecewise-constant scattering length. We use a “stitching” approach to analytically approximate the pertinent solutions of the underlying nonlinear Schrödinger equation by matching the wave function and its derivatives at the interfaces of the nonlinearity coefficient. To accurately quantify the stability of bright and dark solitons, we adapt general tools from the theory of perturbed Hamiltonian systems. We show that stationary solitons must be …
Experimental Observation Of Oscillating And Interacting Matter Wave Dark Solitons, A Weller, Jp Ronzheimer, C Gross, J Esteve, Mk Oberthaler, Dj Frantzeskakis, G Theocharis, Pg Kevrekidis
Experimental Observation Of Oscillating And Interacting Matter Wave Dark Solitons, A Weller, Jp Ronzheimer, C Gross, J Esteve, Mk Oberthaler, Dj Frantzeskakis, G Theocharis, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We report on the generation, subsequent oscillation and interaction of a pair of matter-wave dark solitons. These are created by releasing a Bose-Einstein condensate from a double well potential into a harmonic trap in the crossover regime between one dimension and three dimensions. Multiple oscillations and collisions of the solitons are observed, in quantitative agreement with simulations of the Gross-Pitaevskii equation. An effective particle picture is developed and confirms that the deviation of the observed oscillation frequencies from the asymptotic prediction νz/√2, where νz is the longitudinal trapping frequency, results from the dimensionality of the system and the soliton interactions.
Averaging Of Nonlinearity Management With Dissipation, S Beheshti, Kjh Law, Pg Kevrekidis, Ma Porter
Averaging Of Nonlinearity Management With Dissipation, S Beheshti, Kjh Law, Pg Kevrekidis, Ma Porter
Mathematics and Statistics Department Faculty Publication Series
Motivated by recent experiments in optics and atomic physics, we derive an averaged nonlinear partial differential equation describing the dynamics of the complex field in a nonlinear Schrödinger model in the presence of a periodic nonlinearity and a periodically varying dissipation coefficient. The incorporation of dissipation in our model is motivated by experimental considerations. We test the numerical behavior of the derived averaged equation by comparing it to the original nonautonomous model in a prototypical case scenario and observe good agreement between the two.
Dynamical Barrier For The Formation Of Solitary Waves In Discrete Lattices, Pg Kevrekidis, Ja Espinola-Rocha, Y Drossinos, A Stefanov
Dynamical Barrier For The Formation Of Solitary Waves In Discrete Lattices, Pg Kevrekidis, Ja Espinola-Rocha, Y Drossinos, A Stefanov
Mathematics and Statistics Department Faculty Publication Series
We consider the problem of the existence of a dynamical barrier of “mass” that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schrödinger lattice. We contrast the existence of a dynamical barrier with its absence in the static theory of localized modes in one spatial dimension. We suggest an energetic criterion that provides a sufficient, but not necessary, condition on the amplitude of a single-site initial condition required to form a solitary wave. We show that this effect is not one-dimensional by considering its two-dimensional analog. …
Hecke Operators And Hilbert Modular Forms, Pe Gunnells, D Yasaki
Hecke Operators And Hilbert Modular Forms, Pe Gunnells, D Yasaki
Mathematics and Statistics Department Faculty Publication Series
Let F be a real quadratic field with ring of integers O and with class number 1. Let Γ be a congruence subgroup of GL2 (O)GL2() . We describe a technique to compute the action of the Hecke operators on the cohomology H3 (G; \mathbb C)H3(;C) . For F real quadratic this cohomology group contains the cuspidal cohomology corresponding to cuspidal Hilbert modular forms of parallel weight 2. Hence this technique gives a way to compute the Hecke action on these Hilbert modular forms.
Discrete Solitons And Vortices In Hexagonal And Honeycomb Lattices: Existence, Stability, And Dynamics, Kjh Law, Pg Kevrekidis, V Koukouloyannis, I Kourakis, Dj Frantzeskakis, Ar Bishop
Discrete Solitons And Vortices In Hexagonal And Honeycomb Lattices: Existence, Stability, And Dynamics, Kjh Law, Pg Kevrekidis, V Koukouloyannis, I Kourakis, Dj Frantzeskakis, Ar Bishop
Mathematics and Statistics Department Faculty Publication Series
We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schrödinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and three-lattice-site contours in the form of both discrete multipole solitons and discrete vortices. Additionally to identifying the possible states, we analytically track their linear stability both qualitatively and quantitatively. We find that among the six-site configurations, the “hexapole” of alternating phases (0-π), as well as the vortex of topological charge S=2 have intervals of stability; among three-site states, only the vortex of topological charge S=1 may be stable in …
High-Speed Kinks In A Generalized Discrete Phi(4) Model, Sv Dmitriev, A Khare, Pg Kevrekidis, A Saxena, L Hadzievski
High-Speed Kinks In A Generalized Discrete Phi(4) Model, Sv Dmitriev, A Khare, Pg Kevrekidis, A Saxena, L Hadzievski
Mathematics and Statistics Department Faculty Publication Series
We consider a generalized discrete ϕ4 model and demonstrate that it can support exact moving kink solutions in the form of tanh with an arbitrarily large velocity. The constructed exact moving solutions are dependent on the specific value of the propagation velocity. We demonstrate that in this class of models, given a specific velocity, the problem of finding the exact moving solution is integrable. Namely, this problem originally expressed as a three-point map can be reduced to a two-point map, from which the exact moving solutions can be derived iteratively. It was also found that these high-speed kinks can be …
Highly Nonlinear Solitary Waves In Periodic Dimer Granular Chains, Ma Porter, C Daraio, Eb Herbold, I Szelengowicz, Pg Kevrekidis
Highly Nonlinear Solitary Waves In Periodic Dimer Granular Chains, Ma Porter, C Daraio, Eb Herbold, I Szelengowicz, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We investigate the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic arrangements of particles in experiments in which stiffer and heavier beads (stainless steel) are alternated with softer and lighter ones (polytetrafluoroethylene beads). We find good agreement between experiments and numerics in a model with Hertzian interactions between adjacent beads, which in turn agrees very well with a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments and general bead interactions. Our analysis encompasses previously studied examples as special cases and …
Emergence Of Unstable Modes In An Expanding Domain For Energy-Conserving Wave Equations, Kjh Law, Pg Kevrekidis, Dj Frantzeskakis, Ar Bishop
Emergence Of Unstable Modes In An Expanding Domain For Energy-Conserving Wave Equations, Kjh Law, Pg Kevrekidis, Dj Frantzeskakis, Ar Bishop
Mathematics and Statistics Department Faculty Publication Series
Motivated by recent work on instabilities in expanding domains in reaction–diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider a nonlinear Schrödinger equation in a finite domain and show how the expansion or contraction of the domain, under appropriate conditions, can destabilize its originally stable solutions through the modulational instability mechanism. Using both real and Fourier space diagnostics, we monitor and control the crossing of the instability threshold and, hence, the activation of the instability. We also consider how the manifestation of this mechanism is modified in a spatially inhomogeneous setting, namely …
Sequences Of Willmore Surfaces, K Leschke, F Pedit
Sequences Of Willmore Surfaces, K Leschke, F Pedit
Mathematics and Statistics Department Faculty Publication Series
In this paper we develop the theory of Willmore sequences for Willmore surfaces in the 4-sphere. We show that under appropriate conditions this sequence has to terminate. In this case the Willmore surface either is the Twistor projection of a holomorphic curve into \mathbbC\mathbbP3CP3 or the inversion of a minimal surface with planar ends in \mathbbR4R4. These results give a unified explanation of previous work on the characterization of Willmore spheres and Willmore tori with non-trivial normal bundles by various authors.
Stability Of Discrete Dark Solitons In Nonlinear Schrödinger Lattices, D E. Pelinovsky, Pg Kevrekidis
Stability Of Discrete Dark Solitons In Nonlinear Schrödinger Lattices, D E. Pelinovsky, Pg Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We obtain new results on the stability of discrete dark solitons bifurcating from the anti-continuum limit of the discrete nonlinear Schrödinger equation, following the analysis of our previous paper (2005 Physica D 212 1–19). We derive a criterion for the stability or instability of discrete dark solitons from the limiting configuration and confirm this criterion numerically. We also develop asymptotic calculations of the relevant eigenvalues for a number of prototypical configurations and illustrate their good agreement with the numerical data.
On The P-Parts Of Quadratic Weyl Group Multiple Dirichlet Series, G Chinta, S Friedberg, Pe Gunnells
On The P-Parts Of Quadratic Weyl Group Multiple Dirichlet Series, G Chinta, S Friedberg, Pe Gunnells
Mathematics and Statistics Department Faculty Publication Series
Let Φ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Φ is a Dirichlet series in r complex variables s1,…, sr , initially converging for (si) sufficiently large, which has meromorphic continuation to r and satisfies functional equations under the transformations of r corresponding to the Weyl group of Φ. Two constructions of such series are available, one [B. Brubaker, D. Bump, G. Chinta, S. Friedberg, and J. Hoffstein, Weyl group multiple Dirichlet series I, in: Multiple Dirichlet Series, Automorphic Forms, and Analytic …
Structure And Stability Of Two-Dimensional Bose-Einstein Condensates Under Both Harmonic And Lattice Confinement, Kjh Law, Pg Kevrekidis, Bp Anderson, R Carretero-Gonzalez, Dj Frantzeskakis
Structure And Stability Of Two-Dimensional Bose-Einstein Condensates Under Both Harmonic And Lattice Confinement, Kjh Law, Pg Kevrekidis, Bp Anderson, R Carretero-Gonzalez, Dj Frantzeskakis
Mathematics and Statistics Department Faculty Publication Series
In this work, we study two-dimensional Bose–Einstein condensates confined by both a cylindrically symmetric harmonic potential and an optical lattice with equal periodicity in two orthogonal directions. We first identify the spectrum of the underlying two-dimensional linear problem through multiple-scale techniques. Then, we use the results obtained in the linear limit as a starting point for the existence and stability analysis of the lowest energy states, emanating from the linear ones, in the nonlinear problem. Two-parameter continuations of these states are performed for increasing nonlinearity and optical lattice strengths, and their instabilities and temporal evolution are investigated. It is found …
Symmetry-Breaking Bifurcation In Nonlinear Schrodinger/Gross-Pitaevskii Equations, Ew Kirr, Pg Kevrekidis, E Shlizerman, Mi Weinstein
Symmetry-Breaking Bifurcation In Nonlinear Schrodinger/Gross-Pitaevskii Equations, Ew Kirr, Pg Kevrekidis, E Shlizerman, Mi Weinstein
Mathematics and Statistics Department Faculty Publication Series
We consider a class of nonlinear Schrödinger/Gross–Pitaeveskii (NLS-GP) equations, i.e., NLS with a linear potential. NLS-GP plays an important role in the mathematical modeling of nonlinear optical as well as macroscopic quantum phenomena (BEC). We obtain conditions for a symmetry-breaking bifurcation in a symmetric family of states as ${\cal N}$, the squared $L^2$ norm (particle number, optical power), is increased. The bifurcating asymmetric state is a “mixed mode” which, near the bifurcation point, is approximately a superposition of symmetric and antisymmetric modes. In the special case where the linear potential is a double well with well-separation $L$, we estimate ${\cal …