Abstract
For the solitary-wave solution u(ξ) = u(x − vt + ¾0) to the generalized Pochhammer-Chree equation (PC equation)
the formula\(\int_{ - \infty }^{ + \infty } {[u'(\xi )]^2 d\xi = } \frac{1}{{12r\nu }}(C_ + - C_ - )^3 [3a_3 (C_ + - C_ - ) + 2a_2 ], C_ \pm = \mathop {\lim }\limits_{\xi \to \pm \infty } u(\xi )\), is established, by which it is shown that the generalized PC equation (I) does not have bell profile solitary-wave solutions but may have kink profile solitary-wave solutions. However a special generalized PC equation
may have not only bell profile solitary-wave solutions, but also kink profile solitary-wave solutions whose asymptotic values satisfy 3a3(C++C−)+2a2=0. Furthermore all expected solitary-wave solutions are given. Finally some explicit bell profile solitary-wave solutions to another generalized PC equation
are proposed.
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References
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Communicated by Dai Shiqiang
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Weiguo, Z., Wenxiu, M. Explicit solitary-wave solutions to generalized Pochhammer-Chree equations. Appl Math Mech 20, 666–674 (1999). https://doi.org/10.1007/BF02464941
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DOI: https://doi.org/10.1007/BF02464941
Key words
- nonlinear evolution equation
- generalized Pochhammer-Chree equation
- solitary-wave solution
- exact solution