利用函数不变集方法求解KdV型方程  

New Exact Solutions to KdV-type Equation by the Invariant Set

作　　者：屈改珠[1,2] 张同琦[1] 余保民[1] 

机构地区：[1]渭南师范学院数学与信息科学学院,渭南714000 [2]西北大学数学系,西安710069

出　　处：《工程数学学报》2013年第3期400-406,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10671156);渭南师范学院科研计划项目(12YKF021)~~

摘　　要：本文讨论KdV型方程的演化不变集和精确解,并分别给出了KdV型方程在旋转群、伸缩群以及其它形式群上不变时满足的条件,导出了KdV型方程中系数函数的约束条件,通过求解约束条件构造KdV型方程的不变解.文中的结果进一步推广了Galaktionov关于非线性演化方程的结论.Abstract： In this paper, we discuss evolutionary invariant sets and exact solutions to KdV-type equations. We derive conditions for the KdV-type equation to be invariant under the rotation group, the scaling group and other-type groups, respectively. We obtain the constraints for the coefficient functions in the KdV-type equation, furthermore, we construct the invariant solution to KdV-type equation by solving these constraints. These conclusions generalize the results of nonlinear evolutionary equations given by Galationov.

关 键 词：KDV型方程 函数不变集 精确解 

分 类 号：O175.29[理学—数学]