(1+1)维色散长波系统的留数对称和相互作用解  

Residual Symmetry and Interaction Solutions of the(1+1)-Dimensional Dispersive Long-wave System

作　　者：张开开 夏亚荣 ZHANG Kaikai;XIA Yarong(School of Science,Xi’an University of Architecture and Technology,Xi’an 710055,China)

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《应用数学》2022年第4期918-926,共9页Mathematica Applicata

基　　金：国家自然科学基金(12001424);中国博士后科学基金(2020M673332)。

摘　　要：利用Painlevé截断展开法获得(1+1)维色散长波系统的留数对称,通过引入适当的延拓系统将留数对称局部化为Lie点对称,并给出与留数对称相关的有限对称变换.此外,证明了(1+1)维色散长波系统是相容Riccati展开(CRE)可解的,并运用相容Riccati展开法的特殊形式相容tanh函数展开(CTE)法解出了色散长波系统的孤子-椭圆余弦波之间的相互作用解,同时选取合适的参数对解作出相应的图像模拟.The truncated Painlevé expansion method is employed to derive the residual symmetry of the(1+1)-dimensional dispersive long-wave system. By introducing an appropriate prolonged system, the residual symmetry is localized to the Lie point symmetry, and the finite symmetry transformation related to the residual symmetry is presented. In addition, it is verified that the(1+1)-dimensional dispersive long-wave system is consistent Riccati expansion(CRE) solvable, and the soliton-cnoidal wave interaction solutions of dispersive long-wave system are obtained by using the special form of CRE-consistent tanhfunction expansion(CTE) method. At the same time, the appropriate parameters are selected to simulate the corresponding solutions.

关 键 词：(1+1)维色散长波系统 留数对称 CRE可解 相互作用解 

分 类 号：O175.29[理学—数学]