Geodesic
Asymptotic analysis of multilump solutions of the~Kadomtsev--Petviashvili-I equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 2, pp. 209-224

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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, Wronskian.
Mots-clés : orthogonal polynomials 
@article{TMF_2018_195_2_a3,
     author = {Jen-Hsu Chang},
     title = {Asymptotic analysis of multilump solutions of {the~Kadomtsev--Petviashvili-I} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {209--224},
     publisher = {mathdoc},
     volume = {195},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_195_2_a3/}
}
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Jen-Hsu Chang. Asymptotic analysis of multilump solutions of the~Kadomtsev--Petviashvili-I equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 2, pp. 209-224. http://geodesic.mathdoc.fr/item/TMF_2018_195_2_a3/