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.
A. R. Seadawy. W. Amer. A. Sayed. "Stability Analysis for Travelling Wave Solutions of the Olver and Fifth-Order KdV Equations." J. Appl. Math. 2014 1 - 11, 2014. https://doi.org/10.1155/2014/839485