Symmetry Reduction and Exact Solutions of the (3+1)-Dimensional
Breaking Soliton Equation |
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Authors: | WANG Ling and DONG Zhong-Zhou |
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Institution: | 1. Department of Mathematics and Computer Science, Chizhou University, Chizhou 247000, China
;2. Shanghai Key Laboratory of Trustworthy Computing,
East China Normal University, Shanghai 200062, China
;3. Key Laboratory of Mathematics Mechanization, Chinese Academy of Sciences, Beijing 100080, China |
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Abstract: | By means of the generalized direct method, a relationship is
constructed between the new solutions and the old ones of the
(3+1)-dimensional breaking soliton equation. Based on the
relationship, a new solution is obtained by using a given
solution of the equation. The symmetry is also obtained for the
(3+1)-dimensional breaking soliton equation. By using the equivalent
vector of the symmetry, we construct a seven-dimensional symmetry
algebra and get the optimal system of group-invariant solutions. To
every case of the optimal system, the (3+1)-dimensional breaking
soliton equation is reduced and some solutions to the reduced
equations are obtained. Furthermore, some new explicit solutions are
found for the (3+1)-dimensional breaking soliton equation. |
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Keywords: | generalized direct method breaking soliton equation optimal system explicit solution |
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