用双曲函数法，成功得到了非线性浅水长波近似方程组的精确孤立波解。
We successfully derived some exact solitary wave solutions of the nonlinear approximate equations with long waves in shallow water by using the hyperbola function method.
在光与二能级原子系统相互作用的基础上，我们导出相互作用孤立波方程组及其精确解，以及存在解的两个必要条件。
On the basis of light interaction with two-level atomic system, we derive the interaction solitary wave equations, its solution and two necessary conditions for the existence of the solution.
通过相图中的各种轨道，获得了孤立波，扭子波和周期波的精确解。
By the orbit in the phase portraits, different kinds of solitary wave, kink wave and periodic wave solutions are obtained.
用行波方法得到了这些方程的显式精确解，即有理分式型孤立波解。
The exact and explicit solutions of these equations are obtained by using the travelling wave method. These exact solutions are solitary wave solutions of a rational type.
用行波方法得到了这些方程的显式精确解，即有理分式型孤立波解。
The exact and explicit solutions of these equations are obtained by using the travelling wave method. These exact solutions are solitary wave solutions of a rational type.
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