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

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.


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