基于双线性算子计算Boussinesq方程的孤子解

The soliton solution of Boussinesq equation based on bilinear operator

文章通过引入双线性算子,经等价变换得到双线性算子表示下的Boussinesq方程.将幂级数表示的函数代入变换后的方程求得方程的单孤子、双孤子、N孤子以及一般方程的解析解,并用三维图像成功展示了单孤子、双孤子随时间变化的相互作用过程,结果推广了方程的非线性解.Boussinesq方程孤子解析解及其三维显示,有助于对波浪破碎模型和水深变化方程的理解.

The nonlinear Boussinesq equation is transformed and expressed by using bilinear operator.The soliton solutions are obtained through the function expanded by series,and then,the interaction of them is showed up in 3-D figure.Meanwhile,the soliton solutions of the equation help us to learn more about the wave fraction model and the equation with variation of the deep of the water.