Explicit solutions from residual symmetry of the Boussinesq equation

Xi-Zhong Liu, Jun Yu, Bo Ren
2015 Chinese Physics B  
The Bäcklund transformation related symmetry is nonlocal, which is hard to be applied in constructing solutions for nonlinear equations. In this paper, the residual symmetry of the Boussinesq equation is localized to Lie point symmetry by introducing multiple new variables. By applying the general Lie point method, two main results are obtained: a new type of Bäcklund transformation is derived, from which new solutions can be generated from old ones; the similarity reduction solutions as well
more » ... solutions as well as corresponding reduction equations are found. The localization procedure provides an effective way to investigate interaction solutions between nonlinear waves and solitons.
doi:10.1088/1674-1056/24/3/030202 fatcat:3y3tvxun5fdujgvmcwjjn5cwry