×

A note on the existence of solitary waves to the regularized Benjamin-Ono Zakharov-Kuznetsov (rBO-ZK) equation. (English) Zbl 1343.35055

Summary: we examine the existence of solitary waves to the following equation \[ u_t+ a(u^n)_x+ (b{\mathcal H}u_t+ u_{yy})_x= 0, \] where \({\mathcal H}\) 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.

MSC:

35C08 Soliton solutions
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35G25 Initial value problems for nonlinear higher-order PDEs
42B35 Function spaces arising in harmonic analysis
35Q53 KdV equations (Korteweg-de Vries equations)
PDFBibTeX XMLCite
Full Text: DOI