Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Jian Yang, Xiaojuan Lu and Shengqiang Tang
Pages: [1] - [13]
Received Date: November 28, 2014
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121422
By using transformation 
the method of sine-cosine and the method of
dynamical bifurcation theory of the differentiable dynamics, we study
the generalized Kuramoto-Sivashinsky equation. It is shown that the
generalized Kuramoto-Sivashinsky equation gives solitary wave
solution, solitary patterns wave solution, and periodic wave solution.
Under different parametric conditions, various sufficient conditions
to guarantee the existence of the above solutions are given. All exact
explicit parametric representations of the above waves are determined.
solitary wave, periodic wave, solitary patterns wave, method of sine-cosine, method of dynamical bifurcation theory of the differentiable dynamics, generalized Kuramoto-Sivashinsky equation.
