变系数(2+1)维分散长波方程的精确类孤子解  

Exact solutions to the (2 +1)-dimensional dispersive long wave equations

作　　者：关红阳[1] 王振[2] 

机构地区：[1]辽宁中医药大学信息工程学院,辽宁沈阳110847 [2]大连理工大学数学科学学院,辽宁大连116024

出　　处：《辽宁工程技术大学学报（自然科学版）》2017年第8期892-896,共5页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金(51579040;51379033);中央高校基本科研业务费(DUT2015LK30;DUT2015LK43)

摘　　要：为给出非线性偏微分方程的更多精确类孤子解,采用了投影Ricatti方程作为辅助方程,首先推导出了投影Ricatti方程的另外一种形式,证明这种特殊形式的解可以得到著名辅助方程φ~4方程的所有解,研究结果表明,投影Ricatti方程的这种另外形式的解是辅助方程φ~4方程解的统一形式.同时,以变系数(2+1)维分散长波方程为例,利用此方法借助Maple软件获得了多个新的类孤子解.研究结论初步构造了常用辅助方程新的形式,有助于给出非线性偏微分方程的新的精确类孤子解.Abstract： For obtaining more soliton-like solutions to the nonlinear partial differential equations, this paper firstly provides another form of projective Ricatti equation which is a common auxiliary equation, and proofs that the solutions of the special form of the projective Ricatti equation are equivalent to solutions of φ4 equation. The results prove the uniform solutions of φ4 equation. These solutions are more general. Finally, this paper considers the （2＋1）-dimensional dispersive long wave equations and gets its more exact solutions by the uniform solutions of projective Ricatti equation and Maple. Our research preliminary constructs the new form of auxiliary equation which can get more new soliton-like solutions to the nonlinear partial differential equations. Key words： projective Ricatti equation; （2＋1）-dimensional dispersive long wave equations; φ4 equation; auxiliary equation; soliton-like solutions

关 键 词：投影Ricatti方程 变系数(2+1)维分散长波方程 φ4方程 辅助方程 精确类孤子解 

分 类 号：O175.2[理学—数学]