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We analyze perturbed version of the complex Toda chain (CTC) in an attempt to describe the adiabatic N - soliton train interactions of the perturbed nonlinear Schr\"odinger equation (NLS). We study perturbations with weak quadratic and…

Other Condensed Matter · Physics 2009-11-10 V. S. Gerdjikov , B. B. Baizakov , M. Salerno

Perturbed version of the complex Toda chain (CTC) has been employed to describe adiabatic interactions within N-soliton train of the nonlinear Schrodinger equation (NLS). Perturbations induced by weak quadratic and periodic external…

Other Condensed Matter · Physics 2009-11-11 V. S. Gerdjikov , B. B. Baizakov , M. Salerno , N. A. Kostov

We investigate the asymptotic behavior of the Manakov soliton trains perturbed by cross-modulation in the adiabatic approximation. The multisoliton interactions in the adiabatic approximation are modeled by a generalized Complex Toda chain…

Exactly Solvable and Integrable Systems · Physics 2016-10-27 V. S. Gerdjikov , M. D. Todorov , A. V. Kyuldjiev

We consider the asymptotic behavior of the soliton solutions of Manakov's system perturbed by external potentials. It has already been established that its multisoliton interactions in the adiabatic approximation can be modeled by the…

Mathematical Physics · Physics 2014-08-05 V. S. Gerdjikov , M. D. Todorov , A. V. Kyuldjiev

The adiabatic N-soliton train interactions for the scalar nonlinear Schrodinger (NLS) equation and its perturbed versions are well studied. Here we briefly outline how they can be generalized for the higher NLS-type equations and for the…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 V. S. Gerdjikov

Using the Karpman-Solov'ev method we derive the equations for the 2-soliton adiabatic interaction for solitons of the modified nonlinear Schrodinger equation (MNSE). Then we generalize these equations to the case of N interacting solitons…

Exactly Solvable and Integrable Systems · Physics 2009-11-07 V. S. Gerdjikov , E. V. Doktorov , J. Yang

We analyze the dynamical behavior of the $N$-soliton train in the adiabatic approximation of the Manakov model. %perturbed by gain/loss effects and also by several types of external potentials. The evolution of Manakov $N$-soliton trains is…

Exactly Solvable and Integrable Systems · Physics 2020-07-22 Vladimir S. Gerdjikov , Michail D. Todorov

Our previous results on the N-soliton interaction in the adiabatic approximation have been extended. It is shown that the complex Toda chain (CTC) model is an universal one in the sense that it describes the N-soliton train interactions for…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 V. S. Gerdjikov , I. M. Uzunov

We investigate soliton collisions in the Manakov model, which is a system of coupled nonlinear Schroedinger equations that is integrable via the inverse scattering method. Computing the asymptotic forms of the general N-soliton solution in…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Takayuki Tsuchida

Using the complex Toda chain (CTC) as a model for the propagation of the N-soliton pulse trains of the nonlinear Schrodinger (NLS) equation, we predict the asymptotic behavior of these trains. The following asymptotic regimes are stable:…

solv-int · Physics 2009-09-25 V. S. Gerdjikov , E. G. Evstatiev , D. J. Kaup , G. L. Diankov , I. M. Uzunov

Dynamics of a chain of interacting parity-time invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of…

We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schroedinger equation under the influence of a small correction to the…

patt-sol · Physics 2009-10-31 James A. Besley , Peter D. Miller , Nail N. Akhmediev

We investigate the effects on solitons dynamics of introducing a PT-symmetric complex potential in a specific family of the cubic Dirac equation in (1+1)-dimensions, called the ABS model. The potential is introduced taking advantage of the…

Pattern Formation and Solitons · Physics 2025-11-12 Franz G. Mertens , Bernardo Sánchez-Rey , Niurka R. Quintero

A new integrable nonlocal nonlinear Schroedinger (NLS) equation with clear physical motivations is proposed. This equation is obtained from a special reduction of the Manakov system, and it describes Manakov solutions whose two components…

Exactly Solvable and Integrable Systems · Physics 2018-10-10 Jianke Yang

We introduce a model based on a system of coupled nonlinear Schrodinger (NLS) equations with opposite signs infront of the kinetic and gradient terms in the two equations. It also includes time-dependent nonlinearity coefficients and a…

Quantum Gases · Physics 2015-07-03 R. Radha , P. S. Vinayagam , J. B. Sudharsan , Boris. A. Malomed

In this paper, the Talbot effect for the multi-component linear and nonlinear systems of the dispersive evolution equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profiles is investigated.…

Analysis of PDEs · Mathematics 2024-06-26 Zihan Yin , Jing Kang , Xiaochuan Liu , Changzheng Qu

Coupled nonlinear Schrodinger equations (CNLS) with an external elliptic function potential model a quasi one--dimensional interacting two-component Bose-Einstein condensate trapped in a standing light wave. New families of stationary…

Soft Condensed Matter · Physics 2007-05-23 N. A. Kostov , V. Z. Enol'skii , V. S. Gerdjikov , V. V. Konotop , M. Salerno

Dynamics of solitons of the Ablowitz-Ladik model in the presence of a random potential is studied. In absence of the random potential it is an integrable model and the solitons are stable. As a result of the random potential this stability…

Disordered Systems and Neural Networks · Physics 2015-01-20 Zhi-Yuan Sun , Shmuel Fishman , Avy Soffer

We investigate soliton mobility in the disordered Ablowitz-Ladik (AL) model and the standard nonlinear Schr\"{o}dinger (NLS) lattice with the help of an effective potential generalizing the Peierls-Nabarro potential. This potential results…

Pattern Formation and Solitons · Physics 2015-09-04 Zhi-Yuan Sun , Shmuel Fishman , Avy Soffer

Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc.. The stable solitons have been captured not only…

Pattern Formation and Solitons · Physics 2017-04-11 Yong Chen , Zhenya Yan
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