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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Skyrmions, Rational Maps & Scaling Identities, E. G. Charalampidis, T. A. Ioannidou, N. S. Manton
Skyrmions, Rational Maps & Scaling Identities, E. G. Charalampidis, T. A. Ioannidou, N. S. Manton
Efstathios Charalampidis
Starting from approximate Skyrmion solutions obtained using the rational map ansatz, improved approximate Skyrmions are constructed using scaling arguments. Although the energy improvement is small, the change of shape clarifies whether the true Skyrmions are more oblate or prolate.
Vortex–Soliton Complexes In Coupled Nonlinear Schrödinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, Panayotis G. Kevrekidis, D. J. Frantzeskakis, B. A. Malomed
Vortex–Soliton Complexes In Coupled Nonlinear Schrödinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, Panayotis G. Kevrekidis, D. J. Frantzeskakis, B. A. Malomed
Efstathios Charalampidis
We consider a two-component, two-dimensional nonlinear Schr¨odinger system with unequal dispersion coefficients and self-defocusing nonlinearities. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component. We show that the potential well may support not only the fundamental bound state, which forms a vortex–bright (VB) soliton, but also multi-ring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states …
Rogue Waves In Nonlinear Schrodinger Models With Variable Coefficients : Application To Bose Einstein Condensates, J. S. He, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskasis
Rogue Waves In Nonlinear Schrodinger Models With Variable Coefficients : Application To Bose Einstein Condensates, J. S. He, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskasis
Efstathios Charalampidis
We explore the form of rogue waves solution sin a select set of case examples of non linear Schrodinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe atomic Bose Einstein condensates in different experimentally relevant settings. For these models, we identify exact rogue waves solutions. Our analytical findings are corroborated by direct numerical integration of the original equations, performed by two different schemes. Very good agreement between numerical results and analytical predictions for the emergence of the rogue waves is identified. Additionally, the nontrivial fate of small numerically induced perturbations …
Dark Bright Solitons In Coupled Nonlinear Schrodinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskaki, B. A. Malomed
Dark Bright Solitons In Coupled Nonlinear Schrodinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskaki, B. A. Malomed
Efstathios Charalampidis
We study a two component nonlinear Schrodinger system with equal, repulsive cubic interactions and different dispersion coefficients in the two components. We consider states that have a dark solitary wave in one component. Treating it as a frozen one, we explore the possibility of the formation of bright solitonic structures in the other component. We identify bifurcation points at which such states emerge in the bright component in the linear limit and explore their continuation into the nonlinear regime. An additional analytically tractable limit is found to be that of vanishing dispersion of the bright component. We numerically identify regimes …
Lattice Three-Dimensional Skyrmions Revisited, E G. Charalampidis, T A. Ioannidou, Panayotis G. Kevrekidis
Lattice Three-Dimensional Skyrmions Revisited, E G. Charalampidis, T A. Ioannidou, Panayotis G. Kevrekidis
Efstathios Charalampidis
In the continuum a skyrmion is a topological nontrivial map between Riemannian manifolds, and a stationary point of a particular energy functional. This paper describes lattice analogues of the aforementioned skyrmions, namely a natural way of using the topological properties of the three dimensional continuum Skyrme model to achieve topological stability on the lattice. In particular, using fixed point iterations, numerically exact lattice skyrmions are constructed; and their stability under small perturbations is explored by means of linear stability analysis. While stable branches of such solutions are identified, it is also shown that they possess a particularly delicate bifurcation structure, …
Vector Rogue Waves And Dark Bright Boomeronic Solitons In Autonomous And Non Autonomous Settings, R. Babu Mareeswaran, E. G. Charalampidis, T. Kanna, P. G. Kevrekidis, D. J. Frantzeskakis
Vector Rogue Waves And Dark Bright Boomeronic Solitons In Autonomous And Non Autonomous Settings, R. Babu Mareeswaran, E. G. Charalampidis, T. Kanna, P. G. Kevrekidis, D. J. Frantzeskakis
Efstathios Charalampidis
In this work, we consider the dynamics of vector rogue waves and ark bright solitons in two component nonlinear Schrodinger equations with various physically motivated time dependent non linearity coefficients, as well as spatio temporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and dark bright boomeron like soliton solutions of the latter are converted back into ones of the original non autonomous model. Using direct numerical simulations we find that, in most cases, the rogue waves formation is rapidly followed by a modulational instability that leads …
Exciting And Harvesting Vibrational States In Harmonically Driven Granular Chains, C. Chong, E. Kim, E. G. Charalampidis, H. Kim, F. Li, Panayotis G. Kevrekidis, J. Lydon, C. Daraio, J. Yang
Exciting And Harvesting Vibrational States In Harmonically Driven Granular Chains, C. Chong, E. Kim, E. G. Charalampidis, H. Kim, F. Li, Panayotis G. Kevrekidis, J. Lydon, C. Daraio, J. Yang
Efstathios Charalampidis
This article explores the excitation of different vibrational states in a spatially extended dynamical system through theory and experiment. As a prototypical example, we consider a one-dimensional packing of spherical particles (a so-called granular chain) that is subject to harmonic boundary excitation. The combination of the multi-modal nature of the system and the strong coupling between the particles due to the nonlinear Hertzian contact force leads to broad regions in frequency where different vibrational states are possible. In certain parametric regions, we demonstrate that the Nonlinear Schrodinger (NLS) equation predicts the corresponding ¨ modes fairly well. We propose that nonlinear …