New exact solution families for forced Boussinesq equation via an extension of generalized tanh-function method

Abstract

In this paper, we present a novel generalization of the tanh method for solving nonlinear partial differential equations, and a subsequent extension. This approach features a tunable parameter p, allowing the obtainable solution families to be tweaked. We derived new tunable families of soliton, non-soliton traveling wave, and plane periodic solutions after applying our method to the forced classical Boussinesq equation, all of which reduce to standard tanh method solutions when p = 1. While our study was limited to 0 ≤ p ≤ 1, future research should explore solutions beyond this range and investigate the applicability of this generalization to other nonlinear systems, particularly those where finding exact solutions is challenging.