IJPAM: Volume 105, No. 3 (2015)

SOLITARY WAVE SOLUTIONS FOR A CLASS
OF DISPERSIVE EQUATIONS

Alex M. Montes
Department of Mathematics
University of Cauca
Popayán, Kra 3 3N-100, COLOMBIA


Abstract. The focus of the present work is the one-dimensional nonlinear equation

\begin{displaymath} u_t-u_{xxt}+u_x+ u_{xxx}+\alpha uu_x=\lambda(uu_{xxx}+2u_xu_{xx}), \end{displaymath} (1)

modeling the wave breaking phenomenon in the shallow water regime. When $\alpha, \lambda>0$, using a variational approximation, we show that ([*]) admits solitary wave solutions which propagate in the negative $x-$direction.

Received: September 19, 2015

AMS Subject Classification: 35Q35, 35Q51, 35A15

Key Words and Phrases: water waves, solitary waves, variational methods

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DOI: 10.12732/ijpam.v105i3.12 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 105
Issue: 3
Pages: 439 - 450


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CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).