On concentration of semi-classical solitary waves for a generalized Kadomtsev-Petviashvili equation

Yuanhong Wei; Yong Li; Xue Yang

doi:10.3934/dcdss.2017059

Article Contents

2017, Volume 10, Issue 5: 1095-1106. Doi: 10.3934/dcdss.2017059

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On concentration of semi-classical solitary waves for a generalized Kadomtsev-Petviashvili equation

a.
School of Mathematics, Jilin University, Changchun 130012, China
b.
School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, China
c.
State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130012, China

^* Corresponding author: Yuanhong Wei
^* Corresponding author: Yuanhong Wei

Received: October 31, 2016

Revised: October 31, 2016

Published: October 2017

Y. Wei is supported by NSFC(grant No. 11301209). Y. Li is supported by National Basic Research Program of China (grant No. 2013CB834100), NSFC(grant No. 11571065) and NSFC(grant No. 11171132). X. Yang is supported by NSFC(grant No. 11201173)

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Abstract

The present paper is concerned with semi-classical solitary wave solutions of a generalized Kadomtsev-Petviashvili equation in $\mathbb{R}^{2}$. Parameter $\varepsilon$ and potential $V(x,y)$ are included in the problem. The existence of the least energy solution is established for all $\varepsilon>0$ small. Moreover, we point out that these solutions converge to a least energy solution of the associated limit problem and concentrate to the minimum point of the potential as $\varepsilon \to 0$.

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Mathematics Subject Classification: Primary: 35A15; Secondary: 35Q53.

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