应用改进的试探函数法求得(3+1)维Jimbo-Miwa方程和非线性传输线电位方程的 精确解,包括双曲函数解、三角函数解。对双曲函数解中的参数取特殊值时,可以得到 孤立波解;对三角函数解中的参数取特殊值时,可以得到对应的周期波函数解。实践证明, 试探函数法在非线性数学物理方程领域的应用非常广泛。

Exact solutions of (3+1)-dimensional Jimbo-Miwa equation and nonlinear transmission line potential equation are obtained with improved trial function method, including hyperbolic function and trigonometric function solutions. When parameters in hyperbolic function solutions are taken as some special values, the solitary wave solutions can be obtained. When parameters in trigonometric function solutions are taken as some special values, the periodic wave function solutions can be obtained. Practice proves that the trial function method is widely used in the field of nonlinear mathematical physics equations.