Abundant Symmetries and Exact Compacton-Like Structures in the Two-Parameter Family of the Estevez-Mansfield-Clarkson Equations
Abstract
The two-parameter family of Estevez-Mansfield-Clarkson equations with fully nonlinear dispersion (called E(m,n) equations), (u_z^m)zzτ+γ(u_zn u_τ)_z+uττ=0 which is a generalized model of the integrable Estevez-Mansfield-Clarkson equation uzzzτ+γ(u_zuzτ+uzzu_τ)+uττ=0, is presented. Five types of symmetries of the E(m,n) equation are obtained by making use of the direct reduction method. Using these obtained reductions and some simple transformations, we obtain the solitary-like wave solutions of E(1,n) equation. In addition, we also find the compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they reemerge with the same coherent shape) of E(3, 2) equation and E(m,m-1) for its potentials, say, u_z, and compacton-like solutions of E(m,m-1) equations, respectively. Whether there exist compacton-like solutions of the other E(m,n) equation with m≠ n+1 is still an open problem.
The project supported by National Key Basic Research Development Project Program of China under Grant No. G1998030600, Doctoral Foundation of China under Grant No. 98014119 and National Natural Science Foundation of China under Grant No. 10072013- Publication:
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Communications in Theoretical Physics
- Pub Date:
- January 2002
- DOI:
- 10.1088/0253-6102/37/1/27
- Bibcode:
- 2002CoTPh..37...27Y