Explicit Solitary-Wave Solutions to Generalized Pochhammer-Chree Equations

Zhang Weiguo; Ma Wenxiu

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Zhang Weiguo, Ma Wenxiu. Explicit Solitary-Wave Solutions to Generalized Pochhammer-Chree Equations[J]. Applied Mathematics and Mechanics, 1999, 20(6): 625-632.

Citation:

Zhang Weiguo, Ma Wenxiu. Explicit Solitary-Wave Solutions to Generalized Pochhammer-Chree Equations[J]. Applied Mathematics and Mechanics, 1999, 20(6): 625-632.

Citation:

Zhang Weiguo, Ma Wenxiu. Explicit Solitary-Wave Solutions to Generalized Pochhammer-Chree Equations[J]. Applied Mathematics and Mechanics, 1999, 20(6): 625-632.

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Explicit Solitary-Wave Solutions to Generalized Pochhammer-Chree Equations

Zhang Weiguo¹,
Ma Wenxiu²

1.
Department of Mathematics and Mechanics, Changsha Railway University, Changsha 410075, P R China;
2.
Institute of Mathematics, Fudan University, Shanghai 200433, P R China;

Received Date: 1977-10-20
Rev Recd Date: 1999-02-04
Publish Date: 1999-06-15

Abstract

Abstract

For the solitary-wave solution u(ξ)=u(x-vt+ξ₀)to the generalized Pochhammer-Chree equation(PC equation) u_tt-u_ttxx+ru_xxt-(a₁u+a₂u²+a₃u³)_xx=0,r,a_i=consts(r≠0),(Ⅰ). the formula ∫_-∞^+∞[u'(ξ)]²dξ=1/12rv(C₊-C_-)³[3a₃(C₊+C_-)+2a₂], is established, by which it is shown that the generalized PC equations (Ⅰ) has not bell profile solitary-wave solutions but may have kink profile solitary-wave solutions. However a special generalized PC equation u_tt-u_ttxx-(a₁u+a₂u²+a₃u³)_xx=0 a_i=consts (Ⅱ) 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 so-lutions are given. Finally some explicit bell profile solitary-wave solutions to another generalized PC equation u_tt-u_ttxx-(a₁u+a₃u³+a₅u⁵)_xx=0 a_i=consts are proposed.
- nonlinear evolution equation,
- generalized Pochhammer-Chree equation,
- solitary-wave solution,
- exact solution

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References(3)

References

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