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University of Massachusetts Amherst
Mathematics and Statistics Department Faculty Publication Series
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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Solitary Waves In A Discrete Nonlinear Dirac Equation, Jesús Cuevas–Maraver, Panayotis G. Kevrekidis, Avadh Saxena
Solitary Waves In A Discrete Nonlinear Dirac Equation, Jesús Cuevas–Maraver, Panayotis G. Kevrekidis, Avadh Saxena
Mathematics and Statistics Department Faculty Publication Series
In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross–Neveu model. The motivation for this discrete model proposal is both computational (near the continuum limit) and theoretical (using the understanding of the anti-continuum limit of vanishing coupling). Numerous unexpected features are identified including a staggered solitary pattern emerging from a single site excitation, as well as two- and three-site excitations playing a role analogous to one- and two-site excitations, respectively, of the discrete nonlinear Schrödinger analogue of the model. Stability exchanges between the two- and three-site states …
Pt-Symmetric Dimer In A Generalized Model Of Coupled Nonlinear Oscillators, Jesús Cuevas–Maraver, Avinash Khare, Panayotis G. Kevrekidis, Haitao Xu, Avadh Saxena
Pt-Symmetric Dimer In A Generalized Model Of Coupled Nonlinear Oscillators, Jesús Cuevas–Maraver, Avinash Khare, Panayotis G. Kevrekidis, Haitao Xu, Avadh Saxena
Mathematics and Statistics Department Faculty Publication Series
Abstract In the present work, we explore the case of a general PT -symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schrödinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one …
Vortex Solutions Of The Discrete Gross-Pitaevskii Equation Starting From The Anti-Continuum Limit, J Cuevas, G James, Pg Kevrekidis, Kjh Law
Vortex Solutions Of The Discrete Gross-Pitaevskii Equation Starting From The Anti-Continuum Limit, J Cuevas, G James, Pg Kevrekidis, Kjh Law
Mathematics and Statistics Department Faculty Publication Series
In this paper, we consider the existence, stability and dynamical evolution of dark vortex states in the two-dimensional defocusing discrete nonlinear Schrödinger model, a model of interest both to atomic physics and to nonlinear optics. Our considerations are chiefly based on initializing such vortex configurations at the anti-continuum limit of zero coupling between adjacent sites, and continuing them to finite values of the coupling. Systematic tools are developed for such continuations based on amplitude-phase decompositions and explicit solvability conditions enforcing the vortex phase structure. Regarding the linear stability of such nonlinear waves, we find that in a way reminiscent of …
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 …