Perspective chapter: Families of Seventh-order KdV equations having traveling wave and soliton solutions

Abstract

In this paper, we consider the problem of finding traveling wave solutions to the generalized seventh-order KdV equation (KdV7). Solitons are non-linear waves that exhibit extremely unexpected and interesting behavior—solitary waves that propagate without deformation. We use different approaches in order to find one and multisoliton solutions. Soliton travels through liquid, solid, and gaseous media and even as electron waves through an electromagnetic field. Making use of a traveling wave transformation, we obtain a non-linear ode, which is solved using either hyperbolic or elliptic algorithm. We also use the Hirota method to get the bilinear form, and then we may obtain multisoliton solutions. In the end, we consider the forced KdV7.