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Rational solutions for a (3+1)-dimensional nonlinear evolution equation
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DOI：10.1016/j.cnsns.2019.105116.png)
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Abstract
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A (3+1)-dimensional nonlinear evolution equation is decomposed into three integrable (1+1)-dimensional models, namely, the nonlinear Schrodinger equation, the complex modified Korteweg-de Vries equation and the Lakshmanan-Porsezian-Daniel equation in different dimensions. On basis of a quartet Lax pair, the general Nth-order rational solution in a compact form for this (3+1)-dimensional nonlinear evolution equation is derived by the Darboux transformation method together with the limit approach. These rational solutions up to second order firstly describe the doubly-localized lumps with standard pattern and triangular pattern on a constant background in the (x, y), (y, z) and (x, z) planes. Then, the first-order (fundamental) rogue waves, namely, the line rogue waves on a constant background in the ( y, z) and (x, z) planes are obtained under certain parameter conditions. Furthermore, the multi-rogue waves which are featured with the interaction between several fundamental rogue waves are shown. (C) 2019 Elsevier B.V. All rights reserved.
Keywords:
Rational solution
Rogue wave
Lump solution
Darboux transformation
(3+1)-Dimensional nonlinear evolution equation
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