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We characterize the soliton solutions of the nonlinear Schroedinger equation on the half line with linearizable boundary conditions. Using an extension of the solution to the whole line and the corresponding symmetries of the scattering…

Exactly Solvable and Integrable Systems · Physics 2015-05-13 Gino Biondini , Guenbo Hwang

Although most soliton research has traditionally considered dominant quadratic dispersion, the recent discovery of pure-quartic solitons has inspired analysis of soliton solutions with large higher orders of dispersion. Here we present…

Pattern Formation and Solitons · Physics 2022-08-31 Y. Long Qiang , Tristram J. Alexander , C. Martijn de Sterke

We develop a theory for non-planar interaction between two identical type I spatial solitons propagating at opposite, but arbitrary transverse angles in quadratic nonlinear (or so-called chi(2)) bulk media. We predict quantitatively the…

Pattern Formation and Solitons · Physics 2007-05-23 Steffen Kjaer Johansen , Ole Bang , Mads Peter Soerensen

By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field…

Pattern Formation and Solitons · Physics 2008-01-16 Ivan Christov , C. I. Christov

We use a fractional transformation to connect the traveling wave solutions of the nonlinear Schr\"odinger equation (NLSE), phase-locked with a source, to the elliptic functions satisfying, $f^{\prime\prime}\pm af\pm \lambda f^{3}=0$. The…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 T. Soloman Raju , C. Nagaraja Kumar , Prasanta K. Panigrahi

We propose an integrable system of coupled nonlinear Schrodinger equations with cubic-quintic terms describing the effects of quintic nonlinearity on the ultra-short optical soliton pulse propagation in non-Kerr media. Lax pair, conserved…

solv-int · Physics 2009-10-31 R. Radhakrishnan , A. Kundu , M. Lakshmanan

Soliton solutions are studied for paraxial wave propagation with intensity-dependent dispersion. Although the corresponding Lagrangian density has a singularity, analytical solutions, derived by the pseudo-potential method and the…

Pattern Formation and Solitons · Physics 2020-04-22 Chun-Yan Lin , Jen-Hsu Chang , Gershon Kurizki , Ray-Kuang Lee

This concise review aims to provide a summary of the most relevant recent experimental and theoretical results for solitons, i.e., self-trapped bound states of nonlinear waves, in two- and three-dimensional (2D and 3D) media. In comparison…

Pattern Formation and Solitons · Physics 2023-12-29 Boris A. Malomed

We investigate the dynamics of localized solutions of the relativistic cold fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed…

Plasma Physics · Physics 2014-12-11 E. Siminos , G. Sánchez-Arriaga , V. Saxena , I. Kourakis

We introduce a model of a lossy second-harmonic-generating (chi^2) cavity externally pumped at the third harmonic, which gives rise to driving terms of a new type, corresponding to a cross-parametric gain. The equation for the…

Pattern Formation and Solitons · Physics 2009-11-10 Vitaly Lutsky , Boris A. Malomed

We study large-amplitude one-dimensional solitary waves in photonic crystals featuring competition between linear and nonlinear lattices, with minima of the linear potential coinciding with maxima of the nonlinear pseudopotential, and vice…

We address the issue of mobility of localized modes in two-dimensional nonlinear Schr\"odinger lattices with saturable nonlinearity. This describes e.g. discrete spatial solitons in a tight-binding approximation of two-dimensional optical…

Pattern Formation and Solitons · Physics 2009-11-11 Rodrigo A. Vicencio , Magnus Johansson

We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schr\"odinger models. We show that stability of bright solitons in presence of random perturbations increases dramatically with the…

Pattern Formation and Solitons · Physics 2012-06-07 F. Maucher , W. Krolikowski , S. Skupin

A variation principle is suggested to find self-similar solitary solutions (``solitons'') of shell model of turbulence. For the Sabra shell model the shape of the solitons is approximated by rational trial functions with relative accuracy…

Chaotic Dynamics · Physics 2007-05-23 Victor S. L'vov

A new non-Hermitian E2-quasi-exactly solvable model is constructed containing two previously known models of this type as limits in one of its three parameters. We identify the optimal finite approximation to the double scaling limit to the…

Quantum Physics · Physics 2016-06-10 Andreas Fring

We overview the properties of nonlinear guided waves and (bright and dark) spatial optical solitons in a periodic medium created by a sequence of linear and nonlinear layers. First, we consider a single layer with a cubic nonlinear response…

Pattern Formation and Solitons · Physics 2009-04-01 Andrey A. Sukhorukov , Yuri S. Kivshar

We investigate the propagation and scattering of polaritons in a planar GaAs microcavity in the linear regime under resonant excitation. The propagation of the coherent polariton wave across an extended defect creates phase and intensity…

We develop an exact computational method based on numerical X-propagators for solving polaron models with arbitrary nonlinear couplings of local vibration modes to the electron density and magnitude of the hopping amplitude. Our approach…

Solitons are localised wave disturbances that propagate without changing shape, a result of a nonlinear interaction which compensates for wave packet dispersion. Individual solitons may collide, but a defining feature is that they pass…

Quantum Gases · Physics 2014-12-10 Jason H. V. Nguyen , Paul Dyke , De Luo , Boris A. Malomed , Randall G. Hulet

The interaction of both scalar and counter-rotating polarized steady state pulses (SSP) is studied numerically for a medium characterized by nonlinear susceptibilities of the third and the fifth order (a cubic-quintic medium…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 Sergei O. Elyutin