Abstract

Under the travelling wave transformation, some nonlinear partial differential equations such as the Getmanou equation are transformed to ordinary differential equation. Then using trial equation method and combing complete discrimination system for polynomial, the classifications of all single traveling wave solution to this equation are obtained.

Highlights

  • Many problems in natural and engineering sciences are modeled by partial differential equations (PDE)

  • Looking for the solutions of the equation, especially the exact solutions, is very important. These exact solutions can describe many important phenomena in physics and other fields and help physicists to understand the mechanisms of the complicated physical phenomena

  • I mainly use Liu’s trial equation method and the theory of complete discrimination system for the fouth-order polynomial [10]-[12] to solve exact solutions of the Getmanou equation which has already been solved based on discrimination system of the fifth-order polynomial by Fan [13]

Read more

Summary

Introduction

Many problems in natural and engineering sciences are modeled by partial differential equations (PDE). Looking for the solutions of the equation, especially the exact solutions, is very important. These exact solutions can describe many important phenomena in physics and other fields and help physicists to understand the mechanisms of the complicated physical phenomena. Professor Liu proposed a powerful method named trial equation method [8] [9] for finding exact solutions to nonlinear differential equations. I mainly use Liu’s trial equation method and the theory of complete discrimination system for the fouth-order polynomial [10]-[12] to solve exact solutions of the Getmanou equation which has already been solved based on discrimination system of the fifth-order polynomial by Fan [13].

Application of Trial Equation Method
Classification of the Traveling Wave Solutions
Conclusion
Full Text
Published version (Free)

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