New symmetry reductions, dromions-like and compacton solutions for a 2D BS(m,n) equations hierarchy with fully nonlinear dispersion

作者：Yan ZY^*

来源：Communications in Theoretical Physics, 2002, 37(3): 269-276.

• BS(m, n) equations
• PBS(m, n) equation
• symmetry reduction
• solitary wave solution
• dromion solution
• compacton solution

We have found two types of important exact solutions, compacton solutions, which are solitary waves with the property that after colliding with their own kind, they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction, in the (1+1)D, (1+2)D and even (1+3)D models, and dromion solutions (exponentially decaying solutions in all direction) in many (1+2)D and (1+3)D models. In this paper, symmetry reductions in (1+2)D are considered for the break soliton-type equation with fully nonlinear dispersion (called BS(m, n) equation) u(t) + b(u(m))(xxy) + 4b(u(n)partial derivative(x)(-1)u(y)) = 0, which is a generalized model of (1+2)D break soliton equation u(t) + bu(xxy) + 4buu(y) + 4bu(x)partial derivative(x)(-1)u(y) = 0, by using the extended direct reduction method. As a result, six types of symmetry reductions are obtained. Starting from the reduction equations and some simple transformations, we obtain the solitary wave solutions of BS(1, n) equations, compacton solutions of BS(m, m, - 1) equations and the compacton-like solution of the potential form (called PBS(3, 2)) w(xt) + b(u(x)(m))(xxy) + 4b (w(x)(n)w(y)) x = 0. In addition, we show that the variable integral(x) u(y)dx admits dromion solutions rather than the field u itself in BS(1, n) equation.

• 出版日期2002-3-15
• 单位大连理工大学