三维空间中Zakharov方程的精确解

Exact Solutions to the Zakharov Equations in Three Dimensional Space

运用改进的tanh函数法,利用一种新的Riccati方程得到三维的Zakharov方程的精确解.包括sech型的孤子解、tanh型的孤子解、三角形式的周期解、有理解、Jacobi椭圆函数解.这对验证数值解的正确性以及对方程性质的进一步研究很有意义.

In this paper, by using a new class of Riccati equation and the extended tanhfuction method, exact solutions of the Zakharov in three space dimensions are constructed. The solutions not only include sechsoliton solutions, tanhsoliton solutions, rational solutions, but also include triangle function, periodic solutions and Jacobi ellipse fuction solutions. It is meaningful to the accuracy of the numerical solution as well as the natural further research of this equation.