Abundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh method

摘要

In this work we use the tanh method for solving several forms of the fifth-order nonlinear KdV equation. The forms include the Lax, Sawada–Kotera (SK), Kaup–Kupershmidt (KK), and the Ito forms and other related special cases. Abundant solitons solutions are derived. Two necessary criteria are established to build up reliable strategies that govern the relation between the parameters of the equation. Previously known solutions are recovered and entirely new bell shaped solitons are determined.