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...

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 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...

We consider a higher order nonlinear Schrödinger equation with third- and fourth-order dispersions, cubic–quintic nonlinearities, self steepening, and self-frequency shift effects. This model governs the propagation of femtosecond light pulses in optical fibers. In this paper, we investigate...

We consider the propagation of weakly nonlinear, weakly dispersive waves in an inhomogeneous media within the framework of the variable-coefficient Korteweg-de Vries equation. An analytical formula with which to compute the energy transfer between neighboring solitary waves is derived. The...

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...

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...

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...