Two‐dimensional lump solutions which decay to a uniform state in all directions are obtained for the Kadomtsev–Petviashvili and a two‐dimensional nonlinear Schrödinger type equation. The amplitude of these solutions is rational in its independent variables. These solutions are constructed by taking a ’’long wave’’ limit of the corresponding N‐soliton solutions obtained by direct methods. The solutions describing multiple collisions of lumps are also presented.
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Research Article| July 29 2008
Two‐dimensional lumps in nonlinear dispersive systems
J. Math. Phys. 20, 1496–1503 (1979)
J. Satsuma, M. J. Ablowitz; Two‐dimensional lumps in nonlinear dispersive systems. J. Math. Phys. 1 July 1979; 20 (7): 1496–1503. https://doi.org/10.1063/1.524208
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