Compactons and kink-like solutions of BBM-like equations by means of factorization

TL;DR

This paper applies the factorization method to BBM-like equations with nonlinear dispersion, deriving various wave solutions including compactons and kinks, and linking these to the Lagrangian and Hamiltonian formulations.

Contribution

It introduces a novel application of factorization to find explicit wave solutions of nonlinear BBM-like equations, including compactons and kinks, with associated Lagrangian and Hamiltonian structures.

Findings

Derived traveling wave solutions in terms of Weierstrass functions.

Identified periodic, solitary, compacton, and kink-like solutions.

Established Lagrangian and Hamiltonian formulations for the equations.

Abstract

In this work, we study the Benjamin-Bona-Mahony like equations with a fully nonlinear dispersive term by means of the factorization technique. In this way we find the travelling wave solutions of this equation in terms of the Weierstrass function and its degenerated trigonometric and hyperbolic forms. Then, we obtain the pattern of periodic, solitary, compacton and kink-like solutions. We give also the Lagrangian and the Hamiltonian, which are linked to the factorization, for the nonlinear second order ordinary differential equations associated to the travelling wave equations.