A method is given for finding the shifts in position of the solitons for the case of nonzero reflection coefficient. Expressions for boost generators in terms of scattering data play a prominent role in the analysis. Phase-shift formulas which show the effect of the radiation component on the soliton motion are deduced for the nonlinear Schrodinger equation, the Korteweg —de Vries equation, and...

This article presents a numerical model to study wave turbulence in fluids. The equation is derived by incorporating energy conservation (along with the usual fluid equations of compressible flow), and source nonlinearity rise temperature due acoustic wave's high amplitude. nonlinear Schrödinger (NLS) modified (MNLS) have been then solved numerically. A simulation MNLS used for investigating ge...

A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary...

In order to solve nonlinear kinetic equations for recombination reactions when the production of participating species is driven externally at a time-dependent rate, we establish a framework based on the correspondence between these equations and a Schrodinger-type equation in which the product of the recombination constant with the production rate plays the role of the potential. The required ...

A method of connecting the Korteweg~e Vries (KdV) equation, known from the theory of nonlinear waves, with the SchrOdinger equation was discovered in 1967,Pl This method is applied in the present paper to a study of a periodic problem. We find exact analytical formulae for a class of solutions u (x ,t) such that at any moment in time t the potential u (x ,t) of the Schrodinger operator has only...

Many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. For the efficient solution of the above mentioned problems, linear multistep methods or Runge-Kutta technique are used. For the simulation of chemical procedures the ra...

We have used themodified variational iterationmethod MVIM to find the approximate solutions for some nonlinear initial value problems in the mathematical physics, via the Burgers-Fisher equation, the Kuramoto-Sivashinsky equation, the coupled Schrodinger-KdV equations, and the long-short wave resonance equations together with initial conditions. The results of these problems reveal that the mod...