Remarks on solitary waves of the generalized two dimensional Benjamin-Ono equation
type: Item
instance of: scholarly article
title: Remarks on solitary waves of the generalized two dimensional Benjamin-Ono equation
zbMATH Open document ID: 1236.45008
author: Amin Esfahani
published in: Applied Mathematics and Computation
publication date: 2011-10-11T00:00:00Z
review text: The author studies the two-dimensional generalized Benjamin-Ono equation \[ u_t+ \beta{\mathcal H}u_{xx}+\varepsilon v_y+ u^p u_x= 0,\quad u_y= V_x\tag{1} \] for \((x,y)\in \mathbb{R}^2\), \(t\geq 0\), where \(\varepsilon\) is a constant, \(\beta\in\mathbb{R}\), \({\mathcal H}\) is the Hilbert transform \[ {\mathcal H}u(x,y,t)=\text{p.v. }\pi^{-1} \int_{\mathbb{R}} {u(z,y,t)\over x-z}\,dt, \] p.v. being the Cauchy principal value. The author obtains the conditions of nonexistence of solitary wave solutions \(u\) of (1), proves the existence and regularity property of solitary wave solutions \(u\) of (1) which are continuous and belong to \(C^1_\infty(\mathbb{R}^2)\), studies variational properties of solutions and the nonlinear stability of the solitary waves.
reviewed by: Dan-Mircea Borş
Mathematics Subject Classification ID: 45K05
zbMATH DE Number: 5956388
zbMATH Keywords: nonlinear PDE
zbMATH Keywords: solitary wave solution
zbMATH Keywords: regularity
MaRDI profile type: Publication
full work available at URL: j.amc.2011.05.065
OpenAlex ID: W2138309818
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DOI: 10.1016/J.AMC.2011.05.065
description: scientific article; zbMATH DE number 5956388