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

  • * Corresponding author: Yuanhong Wei

    * Corresponding author: Yuanhong Wei 

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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  • 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 $\varepsilon \to 0$.

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


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