Two-component vector breather solution of the modified BBM equation

2020/05/21 by G. T. Adamashvili, Adamashvili, G. T.
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2005.10569

openalex publication_date 2020/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a continuation of Ref.[1](arXiv:nlin.PS/2001.07758v1). In the present paper, we consider the solution to the modified Benjamin-Bona-Mahony equation u _t + C u_z + βu_zzt + a u² u_z=0 using the generalized perturbation reduction method. The equation is transformed to the coupled nonlinear Schrödinger equations for auxiliary functions. Explicit analytical expression for the shape and parameters of the two-component vector breather oscillating with the sum and difference of frequencies and wavenumbers are obtained.

Related

• Breather solutions of the modified Benjamin-Bona-Mahony equation
• Two-component nonlinear wave of the cubic Boussinesq equation
• Two-component nonlinear wave of the Born-Infeld equation
• Two-component breather solution of the nonlinear wave equation
• Two-component breather solution of the nonlinear Klein-Gordon equation