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Physical Sciences and Mathematics Commons

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Applied Mathematics

2016

Solitons

Articles 1 - 3 of 3

Full-Text Articles in Physical Sciences and Mathematics

Dark Bright Solitons In Coupled Nonlinear Schrodinger Equations With Unequal Dispersion Coefficients, E. G. Charalampidis, P. G. Kevrekidis, D. J. Frantzeskaki, B. A. Malomed Sep 2016

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 …


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 Sep 2016

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 …


On The N-Wave Equations With Pt-Symmetry, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov Jan 2016

On The N-Wave Equations With Pt-Symmetry, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov

Articles

We study extensions of N-wave systems with PT-symmetry. The types of (nonlocal) reductions leading to integrable equations invariant with respect to P- (spatial reflection) and T- (time reversal) symmetries is described. The corresponding constraints on the fundamental analytic solutions and the scattering data are derived. Based on examples of 3-wave (related to the algebra sl(3,C)) and 4-wave (related to the algebra so(5,C)) systems, the properties of different types of 1- and 2-soliton solutions are discussed. It is shown that the PT symmetric 3-wave equations may have regular multi-soliton solutions for some specific choices of their parameters.