An Invariance for (2+1)-Extension of Burgers Equation and Formulae to Obtain Solutions of KP Equation |
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Authors: | TIAN Yong-Bo TIAN Chou SHAO Nan |
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Institution: | 1. Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
;2. Department of Chemistry, University of Science and Technology of China, Hefei 230026, China |
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Abstract: | In this article, we study the (2+1)-extension of Burgers equation and the KP equation. At first, based on a known Bäcklund transformation and corresponding Lax pair, an invariance which depends on two arbitrary functions
for (2+1)-extension of Burgers equation is worked out. Given a known solution and using the invariance, we can find solutions of the (2+1)-extension of Burgers equation repeatedly. Secondly, we put forward an invariance of Burgers equation which cannot be directly obtained by constraining the invariance of the (2+1)-extension of Burgers equation. Furthermore, we reveal that the invariance for finding the solutions of Burgers equation can
help us find the solutions of KP equation. At last, based on the
invariance of Burgers equation, the corresponding recursion
formulae for finding solutions of KP equation are digged out. As
the application of our theory, some examples have been put forward in this
article and some solutions of the (2+1)-extension of Burgers
equation, Burgers equation and KP equation are obtained. |
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Keywords: | invariance (2+1)-extension of Burgers equation formulae for obtaining solutions of KP equation |
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