应用辅助方程法求Zakharov方程的精确解  

Derivation of Exact Solutions for Zakharov Equation with Auxiliary Equation Method

作　　者：杨娟[1] 尹海峰[2] 冯庆江[1] 

机构地区：[1]凯里学院数学科学学院,贵州凯里556011 [2]凯里学院物理与电子工程学院,贵州凯里556011

出　　处：《应用数学》2017年第2期322-329,共8页Mathematica Applicata

基　　金：国家自然科学基金(11464023);凯里学院2014年重点学科(数学)(KZD2014004)

摘　　要：应用辅助方程法求得Zakharov方程的精确解,这些解包括双曲函数解、三角函数解.当对双曲函数解中的参数取特殊值时,可得到孤立波解:当对三角函数解中的参数取特殊值时,可得到周期波函数解.实践表明:辅助方程法在非线性光学、量子光学、激光物理和等离子体物理等领域具有广泛的应用.Using the auxiliary equation method, the exact solutions for Zakharov equation are constructed. These solutions include hyperbolic function solutions, trigonometric function solutions. When the arbitrary parameters in hyperbolic function solutions are taken as some special values, the solitary wave solutions can be obtained.When the arbitrary parameters in trigonometric function solutions are taken as some special values, the trigonometric function solutions can be expressed as periodic wave solutions.Experience has proved that the auxiliary equation method has a very wide range of applications in the study of optoelectronics, quantum optics, laser physics and plasma physics.

关 键 词：辅助方程法 ZAKHAROV方程 孤立波解 周期波解 

分 类 号：O175.2[理学—数学]