Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations

P. J. S. Pereira, Luís Manuel Trabucho de Campos, N. D. Lopes

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations.
Original languageEnglish
Pages (from-to)783-818
JournalNonlinear Dynamics
Volume82
Issue number1-2
DOIs
Publication statusPublished - Oct 2015

Keywords

  • Asymptotic methods
  • Boussinesq differential equations
  • Solitons
  • Travelling wave solutions

Fingerprint Dive into the research topics of 'Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations'. Together they form a unique fingerprint.

  • Cite this