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We introduce a nonlinear Schroedinger equation (NLSE) which combines the pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a non-conservative cubic one with the first spatial derivative, and an external potential, which helps to…

Plasma Physics · Physics 2020-02-26 E. M. Gromov , B. A. Malomed

Events during transition to turbulence either follow modal or non-modal routes, or combinations of the two. Here, we report a computational investigation of strong freestream excitation caused by a train of convecting vortices. For this TCV…

We report branches of explicit expressions for nonlinear modes in parity-time (PT) symmetric potentials of several types. For the single-well and double-well potentials the found solutions are two-parametric and appear to be stable even…

Pattern Formation and Solitons · Physics 2015-09-30 Zhenya Yan , Zichao Wen , Vladimir V. Konotop

We discuss the response of both moving and trapped solitary wave solutions of a nonlinear two-component nonlinear Schr\"odinger system in 1+1 dimensions to an anti-$\mathcal{PT}$ external periodic complex potential. The dynamical behavior…

Pattern Formation and Solitons · Physics 2021-05-03 Efstathios G. Charalampidis , Fred Cooper , John F. Dawson , Avinash Khare , Avadh Saxena

A symbolic computation technique is developed to calculate adiabatic evolution equations for parameters of the perturbed DNLS/MNLS solitons obtained by the recently developed direct perturbation theory [X.-J. Chen and J. Yang, Phys. Rev. E…

Pattern Formation and Solitons · Physics 2009-11-10 Xiang-Jun Chen , Wa Kun Lam

We study the dynamics of bright and dark matter-wave solitons in the presence of a spatially varying nonlinearity. When the spatial variation does not involve zero crossings, a transformation is used to bring the problem to a standard…

Quantum Physics · Physics 2009-11-13 S. Middelkamp , P. G. Kevrekidis , D. J. Frantzeskakis , P. Schmelcher

In this paper we announce the result of asymptotic dynamics of solitons of nonlinear Schrodinger equations with external potentials. To each local minima of the potential there is a soliton centered around it. Under some conditions on the…

Mathematical Physics · Physics 2007-05-23 Zhou Gang , I. M. Sigal

A numerical exploration of a gain-loss nonlinear Schr\"odinger equation was carried out utilizing over 180000 core hours to conduct more than 10000 unique simulations in an effort to characterize the model's six dimensional parameter space.…

Pattern Formation and Solitons · Physics 2014-02-21 Justin Q. Anderson , Rachel A. Ryan , Mingzhong Wu , Lincoln D. Carr

We study the dynamics of one electron wave packet in a chain with a non-adiabatic electron-phonon interaction. The electron-phonon coupling is taken into account in the time-dependent Schr\"odinger equation by a delayed cubic nonlinearity.…

Other Condensed Matter · Physics 2015-05-13 F. A. B. F. de Moura , Iram Gleria , I. F. dos Santos , M. L. Lyra

We investigate the dynamics of travelling oscillating solitons of the cubic NLS equation under an external spatiotemporal forcing of the form $f(x,t) = a \exp[iK(t)x]$. For the case of time-independent forcing a stability criterion for…

Pattern Formation and Solitons · Physics 2025-11-11 Franz G. Mertens , Niurka R. Quintero , I. V. Barashenkov , A. R. Bishop

We consider a family of regularized defocusing nonlinear Schrodinger (NLS) equations proposed in the context of the cubic NLS equation with a bounded dispersion relation. The time evolution is well-posed if the black soliton is perturbed by…

Analysis of PDEs · Mathematics 2023-04-12 Dmitry E. Pelinovsky , Michael Plum

Consider the nonlinear Schr\"odinger equation (NLS) with a potential with a single negative eigenvalue. It has solitons with negative small energy, which are asymptotically stable, and, if the nonlinearity is focusing, then also solitons…

Analysis of PDEs · Mathematics 2016-02-11 Kenji Nakanishi

In this paper, we present a microscopic derivation of the two-dimensional focusing cubic nonlinear Schr\"odinger equation starting from an interacting $N$-particle system of Bosons. The interaction potential we consider is given by…

Mathematical Physics · Physics 2018-08-01 M. Jeblick , P. Pickl

The soliton dynamics for a general class of nonlinear focusing Schr\"odinger problems in presence of non-constant external (local and nonlocal) potentials is studied by taking as initial datum the ground state solution of an associated…

Analysis of PDEs · Mathematics 2009-11-13 Raffaella Servadei , Marco Squassina

We study the N-N interaction in the framework of the chromo-dielectric soliton model. Here, the long-range parts of the nonabelian gluon self-interactions are assumed to give rise to a color-dielectric function which is parameterized in…

Nuclear Theory · Physics 2008-11-26 W. Koepf , L. Wilets , S. Pepin , Fl. Stancu

We consider the existence of a dynamically stable soliton in the one-dimensional cubic-quintic nonlinear Schr\"odinger model with strong cubic nonlinearity management for periodic and random modulations. We show that the predictions of the…

Other Condensed Matter · Physics 2015-06-25 Fatkhulla Kh. Abdullaev , Josselin Garnier

In this work we mainly consider the dynamics and scattering of a narrow soliton of NLS equation with a potential in $\mathbb{R}^3$, where the asymptotic state of the system can be far from the initial state in parameter space. Specifically,…

Analysis of PDEs · Mathematics 2017-02-15 Qingquan Deng , Avy Soffer , Xiaohua Yao

We investigate the dynamics of solitons of the cubic Nonlinear Schr\"odinger Equation (NLSE) with the following perturbations: non-parametric spatio-temporal driving of the form $f(x,t) = a \exp[i K(t) x]$, damping, and a linear term which…

Pattern Formation and Solitons · Physics 2025-11-11 Franz G. Mertens , Niurka R. Quintero , A. R. Bishop

We theoretically investigate the scattering of bright solitons in a Bose-Einstein condensate on narrow attractive potential wells. Reflection, transmission and trapping of an incident soliton are predicted to occur with remarkably abrupt…

Quantum Gases · Physics 2010-03-25 T. Ernst , J. Brand

We demonstrate that periodic modulation of the nonlinearity coefficient in the discrete nonlinear Schr\"{o}dinger (DNLS) equation can strongly facilitate creation of traveling solitons in the lattice. We predict this possibility in an…

Other Condensed Matter · Physics 2015-05-25 Jesus Cuevas , Boris A. Malomed , Panayotis G. Kevrekidis