The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order ǫ, ǫ ≪ 1, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. Whereas the difference betwe...

In this paper, tanh method is applied to obtain exact solutions for two systems of nonlinear wave equations, namely, two component evolutionary system of homogeneous KdV equations of order 3 (type I as well as type II). Moreover, traveling wave hypothesis is used to obtain sech solution of type II coupled KdV system, in a more general setting. The results show that this method presents exact so...

Abstract: In this paper, the homotopy perturbation method (HPM) is applied to obtain approximate solutions to three systems of nonlinear wave equations, namely, two component evolutionary system of a homogeneous KdV equations of order 3 (type I) as well as (type II), and the generalized coupled Hirota Satsuma KdV. The numerical results show that this method is a powerful tool for solving system...

ABSTRACT. The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order ǫ, ǫ ≪ 1, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. Whereas the differ...

Abstract: In this paper, we demonstrate the effectiveness of the (G ′ G )-expansion method by seeking more exact solutions of the SRLW equation, the (2+1) dimensional PKP equation and the (3+1) dimensional potential-YTSF equation. By the method, the two nonlinear evolution equations are separately reduced to non-linear ordinary differential equations (ODE) by using a simple transformation. As a...

In this work, we develop two new (3+1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation and negative-order KdV-CBS (nKdV-nCBS) equation. The newly developed equations pass the Painlevé integrability test via examining compatibility conditions for each model. We examine dispersion relation derive multiple soliton solutions

We study solitary wave interactions in the Euler–Poisson equations modeling ion acoustic plasmas and their approximation by KdV n-solitons. Numerical experiments are performed and solutions compared to appropriately scaled KdV n-solitons. While largely correct qualitatively the soliton solutions did not accurately capture the scattering shifts experienced by the solitary waves. We propose corre...