Abstract
In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.
Highlights
It is important to seek more exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics
Many powerful methods have been presented such as the inverse scattering method [1], the Darboux transformation [2], the Hirota bilinear method [3], the Painlevé expansion method [4], the Bäcklund transformation method [5, 6], the multilinear variable separation method [7], the homogeneous balance method [8], the Jacobi elliptic function expansion method [9], the tanh-function method [10, 11], the F-expansion method [12], the auxiliary equation method [13], the sub-ODE method [14], the Exp-function method [15], the (G0/G)-expansion method [16, 17], the simplest equation method [18, 19]
Thousands of examples have shown that these methods are powerful for obtaining exact solutions of NLEEs, especially, for traveling wave solutions
Summary
It is important to seek more exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics. Thousands of examples have shown that these methods are powerful for obtaining exact solutions of NLEEs, especially, for traveling wave solutions. Developing new method and finding more general exact solutions of NLEEs have drawn a lot of interests of a diverse group of scientists. N.A. Kudryashov first proposed the simplest equation method and showed that it is powerful for finding analytic solutions of NLEEs [18, 19]. The first idea is to apply the simplest nonlinear differential equations
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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
