Category Ranking
98%
Total Visits
921
Avg Visit Duration
2 minutes
Citations
20
Article Abstract
Discrete solitons in the Ablowitz-Ladik (AL) and discrete nonlinear Schrödinger (DNLS) equations with damping and strong rapid drive are investigated. The averaged equations have the forms of the parametric AL and DNLS equations. An additional type of parametric bright discrete soliton and cnoidal waves are found and the stability properties are analyzed. The analytical predictions of the perturbed inverse scattering transform are confirmed by the numerical simulations of the AL and DNLS equations with rapidly varying drive and damping.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevE.75.016615 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Rogue wave pattern of multi-component derivative nonlinear Schrödinger equations.
Chaos
April 2024
School of Mathematics, South China University of Technology, Guangzhou 510641, China.
This paper studies the multi-component derivative nonlinear Schrödinger (n-DNLS) equations featuring nonzero boundary conditions. Employing the Darboux transformation method, we derive higher-order vector rogue wave solutions for the n-DNLS equations. Specifically, we focus on the distinctive scenario where the (n+1)-order characteristic polynomial possesses an explicit (n+1)-multiple root.
View Article and Find Full Text PDFDiscrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings.
Entropy (Basel)
February 2024
Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica 1000000, Chile.
This article presents a concise survey of basic discrete and semi-discrete nonlinear models, which produce two- and three-dimensional (2D and 3D) solitons, and a summary of the main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ(2)) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of the basic species of multidimensional discrete modes, including fundamental (zero-vorticity) and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.
View Article and Find Full Text PDFThe dynamics of unstable waves in sea ice.
Sci Rep
August 2023
School of Civil Engineering, The University of Sydney, Sydney, NSW, 2006, Australia.
Wave and sea ice properties in the Arctic and Southern Oceans are linked by feedback mechanisms, therefore the understanding of wave propagation in these regions is essential to model this key component of the Earth climate system. The most striking effect of sea ice is the attenuation of waves at a rate proportional to their frequency. The nonlinear Schrödinger equation (NLS), a fundamental model for ocean waves, describes the full growth-decay cycles of unstable modes, also known as modulational instability (MI).
View Article and Find Full Text PDFInverse Scattering Method Solves the Problem of Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model.
Phys Rev Lett
April 2022
Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 9190401, Israel.
We determine the full statistics of nonstationary heat transfer in the Kipnis-Marchioro-Presutti lattice gas model at long times by uncovering and exploiting complete integrability of the underlying equations of the macroscopic fluctuation theory. These equations are closely related to the derivative nonlinear Schrödinger equation (DNLS), and we solve them by the Zakharov-Shabat inverse scattering method (ISM) adapted by D. J.
View Article and Find Full Text PDFEquilibrium and nonequilibrium description of negative temperature states in a one-dimensional lattice using a wave kinetic approach.
Phys Rev E
January 2022
Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Torino, 10125 Torino, Italy.
We predict negative temperature states in the discrete nonlinear Schödinger (DNLS) equation as exact solutions of the associated wave kinetic equation. Within the wave kinetic approach, we define an entropy that results monotonic in time and reaches a stationary state, that is consistent with classical equilibrium statistical mechanics. We also perform a detailed analysis of the fluctuations of the actions at fixed wave numbers around their mean values.
View Article and Find Full Text PDF