Abundant symmetries and exact compacton-like structures in the two-parameter family of the Estevez-Mansfield-Clarkson equations

作者：Yan ZY^*

来源：Communications in Theoretical Physics, 2002, 37(1): 27-34.

• nonlinear evolution equation
• E(m, n) equation
• symmetry reduction
• solitary wave solution
• compacton solution

The two-parameter family of Estevez-Mansfield-Clarkson equations with fully nonlinear dispersion (called E(m, n) equations), (u(x)(m))(xxtau) + gamma (u(z)(n)u(tau))(x) + u(tautau) = 0 which is a generalized model of the integrable Estevez-Mansfield-Clarkson equation u(xxxtau) + gamma(u(z)u(xtau) + u(xx)u(tau)) + u(tautau) = 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(x), 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 not equal n + 1 is still an open problem.

• 出版日期2002-1-15
• 单位大连理工大学