Interaction solutions for a dimensionally reduced Hirota bilinear equation. (English) Zbl 1434.35155
Summary: With the help of Hirota direct method and symbolic computation, two types of interaction solutions to the dimensionally reduced equations in (2+1)-dimensions are derived, respectively, by searching for the solutions to the associated bilinear equations as a combination of positive quadratic function and an exponential/hyperbolic cosine function. It is interesting that the interaction solutions between lump soliton and one stripe soliton generate the fission and fusion phenomena, while the interaction solutions between lump soliton and twin-stripe solitons generate the rogue wave.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 68W30 | Symbolic computation and algebraic computation |
| 35C08 | Soliton solutions |
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