Journal
AIMS MATHEMATICS
Volume 5, Issue 2, Pages 1162-1176Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.2020080
Keywords
generalized (3+1)-dimensional Kadomtsev-Petviashvili equation; bilinear transformation method; mixed lump and soliton solution; asymptotic behavior; fusion and fission
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Funding
- National Natural Science Foundation of China [61702020]
- Beijing Natural Science Foundation [4172013]
- Beijing Natural Science Foundation-Haidian Primitive Innovation Joint Fund [L182007]
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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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