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- Title
Bäcklund transformation, multiple wave solutions and lump solutions to a (3 + 1)-dimensional nonlinear evolution equation.
- Authors
Gao, Li-Na; Zi, Yao-Yao; Yin, Yu-Hang; Ma, Wen-Xiu; Lü, Xing
- Abstract
In this paper, a $$(3+1)$$ -dimensional nonlinear evolution equation is cast into Hirota bilinear form with a dependent variable transformation. A bilinear Bäcklund transformation is then presented, which consists of six bilinear equations and involves nine arbitrary parameters. With multiple exponential function method and symbolic computation, nonresonant-typed one-, two-, and three-wave solutions are obtained. Furthermore, two classes of lump solutions to the dimensionally reduced cases with $$y=x$$ and $$y=z$$ are both derived. Finally, some figures are given to reveal the propagation of multiple wave solutions and lump solutions.
- Subjects
BACKLUND transformations; NONLINEAR evolution equations; MATHEMATICAL variables; NUMERICAL solutions to wave equations; THEORY of wave motion
- Publication
Nonlinear Dynamics, 2017, Vol 89, Issue 3, p2233
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-017-3581-3