非线性弦振动方程的孤子解、周期孤立波解和拟周期解

Soliton solutions,periodic solitary and quasi-periodic wave solutions for a nonlinear vibrating string equation

利用Hirota双线性方法,首先得到了非线性弦振动方程的孤子解,图形分析表明,此方程存在阶梯状的双向孤子解,既包括迎面型碰撞的孤子解,也包括追赶型碰撞的孤子解.其次,得到了非线性弦振动方程4种类型的周期孤立波解.最后,借助于Riemann theta函数,得到了非线性弦振动方程的拟周期解,在极限情况下,该拟周期解可以退化为孤子解.

By using of the Hirota bilinear method,the soliton solutions of the nonlinear vibrating string equation are obtained.The nonlinear vibrating string equation admits up-stair shape bidirectional soliton solutions,which represent the head-on collisions between solitary waves as well as overtaking ones.Then,four types of periodic solitary wave solutions are derived for the nonlinear vibrating string equation.Moreover,the quasi-periodic wave solutions are also given for the nonlinear vibrating string equation by means of the Riemann theta function,under certain limits,the quasi-periodic wave solutions can be reduced to the soliton solutions.