相关论文: Coupled Nonlinear Schr\"{o}dinger equation and Tod…

A system of semi-discrete coupled nonlinear Schr\"{o}dinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse scattering method for the…

In this letter we present an analytic evidence of the non-integrability of the discrete nonlinear Schroedinger equation, a well-known discrete evolution equation which has been obtained in various contexts of physics and biology. We use a…

We investigate the dynamical behavior of continuous and discrete Schrodinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear…

A new integrable system of two symmetrically coupled derivative nonlinear Schroedinger equations is detected by means of the singularity analysis. A nonlinear transformation is proposed which uncouples the equations of the new system.

A discrete version of the inverse scattering method proposed by Ablowitz and Ladik is generalized to study an integrable full-discretization (discrete time and discrete space) of the coupled nonlinear Schr\"{o}dinger equations. The…

We apply the (direct and inverse) prolongation method to a couple of nonlinear Schr{\"o}dinger equations. These are taken as a laboratory field model for analyzing the existence of a connection between the integrability property and loop…

We consider a system of two discrete nonlinear Schr\"{o}dinger equations, coupled by nonlinear and linear terms. For various physically relevant cases, we derive a modulational instability criterion for plane-wave solutions. We also find…

A discrete analogue of the dressing method is presented and used to derive integrable nonlinear evolution equations, including two infinite families of novel continuous and discrete coupled integrable systems of equations of nonlinear…

We prove the existence of non-trivial solutions to a system of coupled, nonlinear, Schroedinger equations with general nonlinearity.

This paper proposes a method for identifying and classifying integrable nonlinear equations with three independent variables, one of which is discrete and the other two are continuous. A characteristic property of this class of equations,…

We generalize the Toda lattice (or Toda chain) equation to the square lattice; i.e., we construct an integrable nonlinear equation, for a scalar field taking values on the square lattice and depending on a continuous (time) variable,…

Linearization of coupled second order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper we describe a simple and straightforward method to…

We reformulate the singularity confinement of the discrete Toda equation. We prove the co-primeness property, which has been introduced in our previous paper (arXiv:1311.0060) as one of the integrability criteria, for the discrete Toda…

The discrete autonomous/non-autonomous Toda equations and the discrete Lotka-Volterra system are important integrable discrete systems in fields such as mathematical physics, mathematical biology and statistical physics. They also have…

Integrable discretisations for a class of coupled (super) nonlinear Schrodinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are…

In this paper, we consider a general form of nonlinear Schr\"{o}dinger equation with time-dependent nonlinearity. Based on the linear eigenvalue problem, the complete integrability of such nonlinear Schr\"{o}dinger equation is identified by…

The method of solving of nonlinear Schr\"odinger equation is considered. Some examples of its applications are demonstrated.

Integrable fractional equations such as the fractional Korteweg-deVries and nonlinear Schr\"odinger equations are key to the intersection of nonlinear dynamics and fractional calculus. In this manuscript, the first discrete/differential…

We have proposed, in our previous papers, a method to characterize integrable discrete soliton equations. In this paper we generalize the method further and obtain a $q$-difference Toda equation, from which we can derive various…

New integrable lattice systems are introduced, their different integrable discretization are obtained. B\"acklund transformations between these new systems and the relativistic Toda lattice (in the both continuous and discrete time…