Abstract
Some explicit travelling wave solutions to constructing exact solutions of nonlinear partial differential equations of mathematical physics are presented. By applying a theory of Frobenius decompositions and, more precisely, by using a transformation method to the coupled Burgers, combined Korteweg-de Vries- (KdV-) modified KdV and Schrödinger-KdV equation is written as bilinear ordinary differential equations and two solutions to describing nonlinear interaction of travelling waves are generated. The properties of the multiple travelling wave solutions are shown by some figures. All solutions are stable and have applications in physics.
Highlights
The investigation of traveling wave solutions of nonlinear evolution equations (NLEEs) plays a vital role in different branches of mathematical physics, engineering sciences, and other technical arenas, such as plasma physics, nonlinear optics, solid state physics, fluid mechanics, chemical physics, and chemistry.The Burgers’ equation has been found to describe various kinds of phenomena such as a mathematical model of turbulence [1] and the approximate theory of flow through a shock wave traveling in viscous fluid [2]
We describe the generalized extended tanhfunction method
In order to seek the traveling wave solutions of (3) and (4), we introduce the following new ansatz: U
Summary
The investigation of traveling wave solutions of nonlinear evolution equations (NLEEs) plays a vital role in different branches of mathematical physics, engineering sciences, and other technical arenas, such as plasma physics, nonlinear optics, solid state physics, fluid mechanics, chemical physics, and chemistry. Various methods have been established to obtain exact traveling solutions of nonlinear partial differential equations, for example, the Jacobi elliptic function expansion method [13], the generalized Riccati equation method [14], the Backlund transformation method [15], the Hirota’s bilinear transformation method [16], the variational iteration method [17,18,19,20], the tanh-coth method [21, 22], the direct algebraic method [23, 24], the Cole-Hopf transformation method [25, 26], the Exp-function method [27,28,29], and others [30].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
