Abstract
We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.
Highlights
In the recent years, investigations of exact solutions to nonlinear partial differential equations (NPDEs) play an important role in the study of nonlinear physical phenomena
We find the exact solutions of (1)
We study the Burgers equation with power-law nonlinearity (2)
Summary
Investigations of exact solutions to nonlinear partial differential equations (NPDEs) play an important role in the study of nonlinear physical phenomena. Conte and Musette [37] presented an indirect method to seek more solitary wave solutions of some NPDEs that can be expressed as polynomials in two elementary functions which satisfy a projective Riccati equation [38]. Using this method, many solitary wave solutions of many NPDEs are found [38, 39]. We will use the generalized projective Riccati equations method to construct exact solutions for the following three nonlinear evolution equations with higherorder nonlinear terms:.
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