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It is commonly held that a necessary condition for the existence of solitons in nonlinear-wave systems is that the soliton's frequency (spatial or temporal) must not fall into the continuous spectrum of radiation modes. However, this is not…

Pattern Formation and Solitons · Physics 2009-10-31 A. R. Champneys , B. A. Malomed , J. Yang , D. J. Kaup

Previous numerical studies have revealed the existence of embedded solitons (ESs) in a class of multi-wave systems with quadratic nonlinearity, families of which seem to emerge from a critical point in the parameter space, where the zero…

Pattern Formation and Solitons · Physics 2009-11-11 B. A. Malomed , T. Wagenknecht , A. R. Champneys , M. J. Pearce

We study localized two- and three-dimensional Langmuir solitons in the framework of model based on generalized nonlinear Schr\"odinger equation that accounts for local and nonlocal contributions to electron-electron nonlinearity. General…

Space Physics · Physics 2007-05-23 T. A. Davydova , A. I. Yakimenko , Yu. A. Zaliznyak

We have found various families of two-dimensional spatiotemporal solitons in quadratically nonlinear waveguide arrays. The families of unstaggered odd, even and twisted stationary solutions are thoroughly characterized and their stability…

Pattern Formation and Solitons · Physics 2009-11-10 Zhiyong Xu , Yaroslav V. Kartashov , Lucian-Cornel Crasovan , Dumitru Mihalache , Lluis Torner

We show the complete integrability and the existence of optical solitons of higher order nonlinear Schrodinger equation by inverse scattering method for a wide range of values of coefficients. This is achieved first by invoking a novel…

solv-int · Physics 2007-05-23 Sasanka Ghosh , Sudipta Nandy

It was recently proved that isolated unstable "embedded lattice solitons" (ELS) may exist in discrete systems. The discovery of these ELS gives rise to relevant questions such as the following: are there continuous families of ELS?, can ELS…

Pattern Formation and Solitons · Physics 2009-11-11 B. A. Malomed , J. Fujioka , A. Espinosa-Ceron , R. F. Rodriguez , S. Gonzalez

We address the nonlinear Schrodinger equation with intensity-dependent dispersion which was recently proposed in the context of nonlinear optical systems. Contrary to the previous findings, we prove that no solitary wave solutions exist if…

Pattern Formation and Solitons · Physics 2021-03-23 R. M. Ross , P. G. Kevrekidis , D. E. Pelinovsky

The existence and stability of stable bright solitons in one-dimensional (1D) media with a spatially periodical modulated Kerr nonlinearity are demonstrated by means of the linear-stability analysis and in direct numerical simulations. The…

Pattern Formation and Solitons · Physics 2019-09-24 Liangwei Zeng , Jianhua Zeng

We study the fractional three-dimensional (3D) nonlinear Schr\"{o}dinger equation with exponential saturating nonlinearity. In the case of the L\'{e}vy index $\alpha=1.9$, this equation can be considered as a model equation to describe…

Pattern Formation and Solitons · Physics 2024-07-09 Volodymyr M. Lashkin , Oleg K. Cheremnykh

The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional…

Pattern Formation and Solitons · Physics 2016-09-08 John D. Carter , Harvey Segur

We theoretically solve the nonlinear Schr\"{o}dinger equation describing the propagation of pure high, even order dispersion (PHEODs) solitons by variational approach. The Lagrangian for nonlinear pulse transmission systems with each…

Optics · Physics 2024-09-12 Xing Liao , Jiahan Huang , Daquan Lu , Wei Hu

We propose a more realistic version of the recently introduced split-step model (SSM), which consists of periodically alternating dispersive and nonlinear segments, by adding uniformly distributed loss and lumped gain to it. In the case…

Pattern Formation and Solitons · Physics 2015-06-26 Rodislav Driben , Boris Malomed

Stability of soliton families in one-dimensional nonlinear Schroedinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of…

Pattern Formation and Solitons · Physics 2016-11-23 Jianke Yang , Sean Nixon

We use the inverse scattering transform, the auto-Backlund transformation and the steepest descent method of Deift and Zhou to obtain the asymptotic stability of the solitons in the cubic NLS (nonlinear Schrodinger) equation.

Dynamical Systems · Mathematics 2013-11-14 Scipio Cuccagna , Dmitry E. Pelinovsky

Black solitons are identical in the nonlinear Schr\"{o}dinger (NLS) equation with intensity-dependent dispersion and the cubic defocusing NLS equation. We prove that the intensity-dependent dispersion introduces new properties in the…

Analysis of PDEs · Mathematics 2022-05-23 Dmitry E. Pelinovsky , Michael Plum

A method for approximating dark soliton solutions of the nonlinear Schrodinger equation under the influence of perturbations is presented. The problem is broken into an inner region, where core of the soliton resides, and an outer region,…

Mathematical Physics · Physics 2015-05-19 Mark J. Ablowitz , Sean D. Nixon , Theodoros P. Horikis , Dimitri J. Frantzeskakis

The existence, stability and other dynamical properties of a new type of multi-dimensional (2D or 3D) solitons supported by a transverse low-dimensional (1D or 2D, respectively) periodic potential in the nonlinear Schr\"{o}dinger equation…

Pattern Formation and Solitons · Physics 2009-11-11 Bakhtiyor B. Baizakov , Boris A. Malomed , Mario Salerno

Existence of a new class of soliton solutions is shown for higher order nonlinear Schrodinger equation, describing thrid order dispersion, Kerr effect and stimulated Raman scattering. These new solutions have been obtaiened by invoking a…

solv-int · Physics 2007-05-23 Sasanka Ghosh , Sudipta Nandy

We study a spherical, self-gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity-induced dispersion, the emergence of solitons becomes possible. We…

Pattern Formation and Solitons · Physics 2024-02-21 G. N. Koutsokostas , S. Sypsas , O. Evnin , T. P. Horikis , D. J. Frantzeskakis

We construct one soliton solutions for the nonlinear Schroedinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) integrability of generalized harmonic oscillators. The soliton wave…

Mathematical Physics · Physics 2010-11-25 Erwin Suazo , Sergei K. Suslov