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Breather solutions in conservative and dissipative nonlinear Klein–Gordon lattices
We study time-periodic and spatially localised solutions (breathers) in general infinite conservative and dissipative nonlinear Klein–Gordon...
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Discrete Breathers of Nonlinear Dimer Lattices: Bridging the Anti-continuous and Continuous Limits
In this work, we study the dynamics of an infinite array of nonlinear dimer oscillators which are linearly coupled as in the classical model of Su,...
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Exponentially fitted methods with a local energy conservation law
A new exponentially fitted version of the discrete variational derivative method for the efficient solution of oscillatory complex Hamiltonian...
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Localization in the Liouville Lattice and Movable Discrete Breathers
AbstractNonlinear differential-difference equations (nonlinear lattices) exhibit single soliton solutions in the form of 1-breathers. These solutions...
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Modulational Instability and Discrete Localized Modes in Two Coupled Atomic Chains with Next-Nearest-Neighbor Interactions
A pair of one dimensional atomic chains which are coupled via the Klein-Gordon potential is considered in this study, with each chain experiencing...
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Interaction Behaviors Between Solitons, Breathers and Their Hybrid Forms for a Short Pulse Equation
In this article, we investigate the dynamical interaction behavior of a short pulse equation in optical fibers with fast-varying packets. We...
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Algebro-geometric Constructions of a Hierarchy of Integrable Semi-discrete Equations
A hierarchy of integrable semi-discrete equations is deduced in terms of the discrete zero curvature equation as well as its bi-Hamiltonian structure...
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A stochastic thermalization of the Discrete Nonlinear Schrödinger Equation
We introduce a mass conserving stochastic perturbation of the discrete nonlinear Schrödinger equation that models the action of a heat bath at a...
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Localised time-periodic solutions of discrete nonlinear Klein–Gordon systems with convex on-site potentials
The existence of nonzero localised periodic solutions for general one-dimensional discrete nonlinear Klein–Gordon systems with convex on-site...
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Existence and Congruence of Global Attractors for Damped and Forced Integrable and Nonintegrable Discrete Nonlinear Schrödinger Equations
We study two damped and forced discrete nonlinear Schrödinger equations on the one-dimensional infinite lattice. Without dam** and forcing they are...
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Effect of Discrete Breathers on the Specific Heat of a Nonlinear Chain
A nonlinear chain with sixth-order polynomial on-site potential is used to analyze the evolution of the total-to-kinetic-energy ratio during...
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Ground States for DNLS Equation with Periodic or Asymptotically Periodic Potential
We study the existence of ground state solutions for a class of discrete nonlinear Schrödinger equation with a sign-changing potential which is...
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The nth-Darboux Transformation and Explicit Solutions of the PT-Symmetry Second-Type Derivative Nonlinear Schrödinger Equation
Non-local problems have become one of the research hotspots in recent years since Ablowitz–Musslimani constructed an integrable non-local nonlinear
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Existence and Stability of Klein–Gordon Breathers in the Small-Amplitude Limit
We consider a discrete Klein–Gordon (dKG) equation on in the limit of the discrete...
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The Derivative Nonlinear Schrödinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms and N-Double-Pole Solutions
In this paper, we report a rigorous theory of the inverse scattering transforms (ISTs) for the derivative nonlinear Schrödinger (DNLS) equation with...
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Riemann–Hilbert Approach and N-Soliton Solutions for a Higher-Order Coupled Nonlinear Schrödinger System
In this paper, the main work is to study the N -soliton solutions for a higher-order coupled nonlinear Schrödinger system by using the method of...
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Standing Waves for Discrete Nonlinear Schrödinger Equations with Nonperiodic Bounded Potentials
In this paper, we investigate standing waves in discrete nonlinear Schrödinger equations with nonperiodic bounded potentials. By using the critical...