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.
"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