New Symmetry Reductions, Dromions-Like and Compacton Solutions for a 2D BS(m, n) Equations Hierarchy

• 作 者: YAN ZhenYa
• 机 构: Department of Applied Mathematics
• 出 处: 理论物理通讯
• 发表日期: 2004年期
• 关键词: BS(m n) equations PBS(m n) equation symmetry reduction solitary wave solution dr

We have found two types of important exact solutions, compacton sohuttions, which are solitary waveswith the property that after colliding with their own kind, they re-emerge with the same coherent shape very much asthe solitons do during a completely elastic interaction, in the (1+1)D, (1+2)D and even (1+3)D models, and dromionsolutions (exponentially decaying solutions in all direction) in many (1+2)D and (1+3)D models. In this paper, symmetryreductions in (1+-2)D are considered for the break soliton-type equation with fully nonlinear dispersion (called BS(m, n)equation) ut + b(um)xxy+ 4b(un uy)x = 0, which is a generalized model of (1+2)D break soliton equation ut +buxxy + 4buuy + 4bux-1uy = 0, by using the extended direct reduction method. As a result, six types of symmetryreductions are obtained. Starting from the reduction equations and some simple transformations, we obtain the solitarywave solutions ofBS(l, n) equations, compacton solutions ofBS(m, m - 1) equations and the compacton-like solution ofthe potential form (called PBS(3, 2)) wxt + b(umx )xxy + 4b(wnxwy)x = 0. In addition, we show that the variable fx uy dxadmits dromion solutions rather than the field u itself in BS(1, n) equation.