Mixed lump and soliton solutions for a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation

Yu-Lan Ma; Bang-Qing Li; Yu-Lan Ma; Bang-Qing Li

doi:10.3934/math.2020080

AIMS Mathematics

2020, Volume 5, Issue 2: 1162-1176. doi: 10.3934/math.2020080

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Research article

Mixed lump and soliton solutions for a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation

Yu-Lan Ma ¹,
Bang-Qing Li ^{2
,
,}

1.
School of Mathematics and Statistics, Beijing Technology and Business University, Beijing, 100048, China
2.
School of Computer and Information Engineering, Beijing Technology and Business University, Beijing, 100048, China

Received: 11 October 2019 Accepted: 14 December 2019 Published: 15 January 2020
MSC : 35Q51, 35Q53, 37K40

Under investigation is a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation which can be used to describe nonlinear wave propagation in dissipative media. Via the bilinear transformation method, the mixed lump and soliton solutions are obtained for the equation. The asymptotic behavior of the mixed solutions are analyzed. Furthermore, the fusion and fission behaviors of the lump and soliton are observed for the first time. The lump and soliton can merge into a whole soliton over time, or, on the contrary, the soliton may differentiate into a lump and a new soliton. During the processes, the amplitude of the lump will greatly vary, while the amplitude of the soliton will change slightly.
Citation: Yu-Lan Ma, Bang-Qing Li. Mixed lump and soliton solutions for a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation[J]. AIMS Mathematics, 2020, 5(2): 1162-1176. doi: 10.3934/math.2020080

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Abstract

Under investigation is a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation which can be used to describe nonlinear wave propagation in dissipative media. Via the bilinear transformation method, the mixed lump and soliton solutions are obtained for the equation. The asymptotic behavior of the mixed solutions are analyzed. Furthermore, the fusion and fission behaviors of the lump and soliton are observed for the first time. The lump and soliton can merge into a whole soliton over time, or, on the contrary, the soliton may differentiate into a lump and a new soliton. During the processes, the amplitude of the lump will greatly vary, while the amplitude of the soliton will change slightly.

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