经典Boussinesq方程的新同宿轨和孤立子解

New homoclinic orbits and soliton solutions for the classical Boussinesq equations

摘要: 考虑了经典的Boussinesq方程.通过线性稳定性分析,证明了经典的“好”Boussinesq方程存在同宿轨解,经典的“坏”Boussinesq方程存在孤立子解.然后,利用Hirota双线性方法,得到了方程的新同宿轨和孤立子解.

Abstract: The classical Boussinesq equations are considered.By the linearized stability analysis,the existences of homoclinic orbits for "good" Boussinesq equation and periodic soliton for "bad" Boussinesq equation are proved.And then using the Hirota’s bilinear method,the explicit expressions of new homoclinic orbits and periodic soliton solutions for the classical Boussinesq equations are obtained.