The coupled nonlinear Schrödinger equation models several intersting physical phenomena. It presents a model equation for optical fiber with linear birefringence. In this paper, we present a linearly implicit conservative method to solve this equation. This method is second order accurate in...

Interest in finding exact solitary wave solutions of nonlinear evolution equations by means of different methods has grown steadily in recent years. These exact solutions are important to understand the mechanism of the complicated nonlinear physical phenomena. By use of the Jacobi elliptic...

In this paper implementations of three numerical schemes for the numerical simulation of the complex modified Korteweg-de Vries (CMKdV) equation are reported. The first is an integrable scheme derived by methods related to the Inverse Scattering Transform (IST). The second is derived from the...

Numerical simulations show that higher order KdV equation under certain conditions has a self-focusing singularity, which means that the solution of the equation blows up in finite time. In this paper, two numerical schemes: the split-step Fourier transform and the pseudospectral methods are...

The variable-coefficient Korteweg-de Vries equation that governs the dynamics of weakly nonlinear long waves in a periodically variable dispersion management media is considered. For general bit patterns, an analytic expression describing the evolution of the timing shift produced by nonlinear...

Propagation of weakly nonlinear long waves in a periodically inhomogeneous medium is considered in the framework of the variable-coefficients Korteweg–de Vries equation. Explicit formulas with which to compute timing and amplitude jitter caused by nonlinear interactions between adjacent...

In this paper a differential-difference equation is derived by methods related to the inverse scattering transform (IST), which has as its limiting form the nonlinear partial differential equation ut+6αuux+6βu2ux + uxxx=0. It is shown that the differential-difference equations which have as...

In this work, a generalized time-dependent variable coefficients combined KdV–mKdV (Gardner) equation arising in plasma physics and ocean dynamics is studied. By means of three amplitude ansatz that possess modified forms to those proposed by Wazwaz in 2007, we have obtained the bell type...

A proposed scheme for the numerical simulation of the Nonlinear Schrödinger (NLS) equation is implemented and compared to other known numerical methods. This proposed scheme is constructed by methods related to the inverse scattering transform (IST). Performance data are used to compare it with...