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TMF, 2018, Volume 195, Number 2, Pages 209–224 (Mi tmf9428)  

Asymptotic analysis of multilump solutions of the Kadomtsev–Petviashvili-I equation

Jen-Hsu Chang

Department of Computer Science and Information Engineering, National Defense University, Tau-Yuan, Taiwan

Abstract: We construct lump solutions of the Kadomtsev–Petviashvili-I equation using Grammian determinants in the spirit of the works by Ohta and Yang. We show that the peak locations depend on the real roots of the Wronskian of the orthogonal polynomials for the asymptotic behaviors in some particular cases. We also prove that if the time goes to $-\infty$, then all the peak locations are on a vertical line, while if the time goes to $\infty$, then they are all on a horizontal line, i.e., a $\pi/2$ rotation is observed after interaction.

Keywords: Grammian determinant, lumps solutions, orthogonal polynomials, Wronskian.

Funding Agency Grant Number
Ministry of Science and Technology, Taiwan 104-2115-M-606-001.
This research is supported by the Ministry of Science and Technology (Grant No. 104-2115-M-606-001).


DOI: https://doi.org/10.4213/tmf9428

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English version:
Theoretical and Mathematical Physics, 2018, 195:2, 676–689

Bibliographic databases:

Document Type: Article
MSC: 37K40
Received: 04.07.2017
Revised: 05.09.2017

Citation: Jen-Hsu Chang, “Asymptotic analysis of multilump solutions of the Kadomtsev–Petviashvili-I equation”, TMF, 195:2 (2018), 209–224; Theoret. and Math. Phys., 195:2 (2018), 676–689

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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