Application of classification of traveling wave solutions to the modified benjamin–bona–mahony equation with power-law

Abstract

Partial differential equations are widely used in scientific and engineering. In this article, based on the differential equations of the reduced order idea (ODE), we apply Professor Liu’s method, whose core idea is reduction of the order of ODE, to solve Modified Benjamin–Bona–Mahony equation with power-law. Under the travelling wave transformation, Modified Benjamin–Bona–Mahony equation with power-law can be turned into ordinary differential equation. By using polynomial completely discriminant classification system, we can give all single traveling wave solutions of this equation classification. These solutions can’t be obtained by any other indirect methods.

Keywords:

• Modified Benjamin–Bona–Mahony equation with power-law
• traveling wave transform
• complete discrimination system for polynomial
• classification