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Exact solutions and residual symmetries of the Ablowitz–Kaup–Newell–Segur system

Chinese Physics B 2015年第1期24卷 125-131页

作者：刘萍曾葆青杨建荣任博 College of Electron and Information Engineering University of Electronic Science and Technology of China Zhongshan Institute School of Physical Electronics University of Electronic Science and Technology of China Department of Physics and Electronics Shangrao Normal University Institute of Nonlinear Science Shaoxing University

The residual symmetries of the Ablowitz-Kaup-Newell-Segur （AKNS） equations are obtained by the truncated Painleve analysis. The residual symmetries for the AKNS equations are proved to be nonlocal and the nonlocal residual symmetries are extended to the local Lie point symmetries of a prolonged AKNS system. The local Lie point symme- tries of the prolonged AKNS equations are composed of the residual symmetries and the standard Lie point symmetries, which suggests that the residual symmetry method is a useful complement to the classical Lie group theory. The calcula- tion on the symmetries shows that the enlarged equations are invariant under the scaling transformations, the space-time translations, and the shift translations. Three types of similarity solutions and the reduction equations are demonstrated. Furthermore, several types of exact solutions for the AKNS equations are obtained with the help of the symmetry method and the Backlund transformations between the AKNS equations and the Schwarzian AKNS equation.

关键词： residual symmetries Ablowitz-Kaup-Newell-Segur equation exact solution Backlund transformation

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The residual symmetry,Bäcklund transformations,CRE integrability and interaction solutions:(2+1)-dimensional Chaffee–Infante equation

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Communications in Theoretical Physics 2023年第11期75卷 30-37页

作者： Nursena Günhan Ay Emrullah Yaşar Department of Mathematics Faculty of Engineering and Natural Sciencesİstanbul Medeniyet University34700ÜsküdarIstanbulTurkey Department of Mathematics Faculty of Arts and SciencesUludag University16059 BursaTurkey

In this paper,we consider the(2+1)-dimensional Chaffee-Infante equation,which occurs in the fields of fluid dynamics,high-energy physics,electronic science *** build Bäcklund transformations and residual symmetries in nonlocal structure using the Painlevétruncated expansion *** use a prolonged system to localize these symmetries and establish the associated one-parameter Lie transformation *** this transformation group,we deliver new exact solution profiles via the combination of various simple(seed and tangent hyperbolic form)exact solution *** this manner,we acquire an infinite amount of exact solution forms ***,we demonstrate that the model may be integrated in terms of consistent Riccati *** the Maple symbolic program,we derive the exact solution forms of solitary-wave and soliton-cnoidal *** 3D and 2D illustrations,we observe the dynamic analysis of the acquired solution forms.

关键词： (2+1)-dimensional Chaffee-Infante equation Painlevétruncated exapansion approach dynamic analysis Bäcklund transformations residual symmetries

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