Solitary wave solutions of nonlinear partial differential equations based on the simplest equation for the function $1/{\cosh }^n$

Abstract

The method of simplest equation is applied for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. The used simplest equation is $f_{\xi }^2=n^2(f^2-f^{(2n+2)/n})$. The developed methodology is illustrated on two examples of classes of nonlinear partial differential equations that contain: (i) only monomials of odd grade with respect to participating derivatives; (ii) only monomials of even grade with respect to participating derivatives. The obtained solitary wave solution for the case (i) contains as particular cases the solitary wave solutions of Korteweg-deVries equation and of a version of the modified Korteweg-deVries equation.

arXiv comment17 pages, no figures

References in corpus (5)

• Simplest equation method to look for exact solutions of nonlinear differential equations
• A model of ideological struggle
• Meromorphic solutions of nonlinear ordinary differential equations
• Nonlinear analysis of time series of vibration data from a friction brake: SSA, PCA, and MFDFA
• Analysis of a Japan government intervention on the domestic agriculture market

Cited by in corpus (1)

• The Simple Equations Method (SEsM) and the use of exponential functions for obtaining simple and multisoliton solutions of some nonlinear partial differential equations