Stability analysis for travelling wave solutions of the Olver and fifth-order KdV equations. (English) Zbl 1406.35336

Seadawy, A. R.; Amer, W.; Sayed, A.

J. Appl. Math. 2014, Article ID 839485, 11 p. (2014).

Summary: The Olver equation is governing a unidirectional model for describing long and small amplitude waves in shallow water waves. The solitary wave solutions of the Olver and fifth-order KdV equations can be obtained by using extended tanh and sech-tanh methods. The present results are describing the generation and evolution of such waves, their interactions, and their stability. Moreover, the methods can be applied to a wide class of nonlinear evolution equations. All solutions are exact and stable and have applications in physics.

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
35C07	Traveling wave solutions
35B35	Stability in context of PDEs