Abstract
Using the methods of dynamical systems for the (n + 1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking bounded wave solutions are obtained. For the double sine-Gordon equation, the exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.
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This work was supported by the National Natural Science Foundation of China (Grant No. 11671179) and the Natural Science Foundation of Yunnan Province (Grant No. 2005A0092M).
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Li, Jb. Exact traveling wave solutions and dynamical behavior for the (n + 1)-dimensional multiple sine-Gordon equation. SCI CHINA SER A 50, 153–164 (2007). https://doi.org/10.1007/s11425-007-2078-9
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DOI: https://doi.org/10.1007/s11425-007-2078-9
Keywords
- nonlinear wave
- bifurcation
- exact explicit traveling wave solution
- double sine-Gordon equation
- multiple sine-Gordon equation