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| Nonlocal Symmetries and Explicit Solutions of theBoussinesq Equation |
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Citation： |
Xiangpeng XIN,Junchao CHEN,Yong CHEN.Nonlocal Symmetries and Explicit Solutions of theBoussinesq Equation[J].Chinese Annals of Mathematics B,2014,35(6):841~856 |
| Page view： 1192
Net amount： 1148 |
Authors： |
Xiangpeng XIN; Junchao CHEN; Yong CHEN; |
Foundation： |
the National Natural Science Foundation of China (Nos. 11275072,
11435005), the Research Fund for the Doctoral Program of Higher Education of China (No.
20120076110024), the Innovative Research Team Program of the National Natural Science Foundation
of China (No. 61321064), the Shanghai Knowledge Service Platform for Trustworthy Internet of
Things (No. ZF1213), the Shanghai Minhang District Talents of High Level Scientific Research Project
and the Talent Fund and K. C. Wong Magna Fund in Ningbo University. |
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| Abstract： |
The nonlocal symmetry of the Boussinesq equation is obtained from the known
Lax pair. The explicit analytic interaction solutions between solitary waves and cnoidal
waves are obtained through the localization procedure of nonlocal symmetry. Some other
types of solutions, such as rational solutions and error function solutions, are given by using
the fourth Painlev′e equation with special values of the parameters. For some interesting
solutions, the figures are given out to show their properties. |
Keywords： |
Nonlocal symmetry, Lax pair, Prolonged system, Explicit solution |
Classification： |
22E05, 34A05, 34A34 |
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