Salazar, Fabián Sánchez; Higuera, Miguel Angel Pachón A note on the existence of solitary waves to the regularized Benjamin-Ono Zakharov-Kuznetsov (rBO-ZK) equation. (English) Zbl 1343.35055 Int. J. Appl. Math. 28, No. 5, 557-565 (2015). 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) Keywords:regularized Benjamin-Ono Zakharov-Kuznetsov equation; solitary waves; mountain pass lemma PDFBibTeX XMLCite \textit{F. S. Salazar} and \textit{M. A. P. Higuera}, Int. J. Appl. Math. 28, No. 5, 557--565 (2015; Zbl 1343.35055) Full Text: DOI