A NOTE ON THE EXISTENCE OF SOLITARY WAVES TO
THE REGULARIZED BENJAMIN-ONO
ZAKHAROV-KUZNETSOV (rBO-ZK) EQUATION
Fabián Sánchez Salazar$^1$, Miguel Angel Pachón Higuera$^2$

$^{1,2}$Department of Mathematics
Universidad Central
Kra. 5 No. 21-38 Bogotá, D.C., COLOMBIA
Abstract. In this paper, we examine the existence of solitary waves to the following equation

\begin{displaymath}u_{t}+a(u^{n})_{x}+(b\mathscr{H}u_{t}+u_{yy})_{x}=0,\end{displaymath}

where $\mathscr{H}$ is the Hilbert transform with respect to $x$, and $a$ and $b$ are real numbers, with $b>0$, via a variant of the mountain pass lemma.
AMS Subject Classification: 35A01, 35G25, 42B35, 35C08
Key Words and Phrases: regularized Benjamin-Ono Zakharov-Kuznetsov equation, solitary waves, mountain pass lemma


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DOI: 10.12732/ijam.v28i5.8

Volume: 28
Issue: 5
Year: 2015