scholarly journals NONLOCAL SYMMETRIES AND EXACT SOLUTIONS OF A VARIABLE COEFFICIENT AKNS SYSTEM

2020 ◽  
Vol 10 (6) ◽  
pp. 2669-2681
Author(s):  
Xiangpeng Xin ◽  
◽  
Lihua Zhang ◽  
Yarong Xia ◽  
Hanze Liu ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Nonlocal Symmetries ◽  
Akns System

Nonlocal symmetries and exact solutions of the (2+1)-dimensional generalized variable coefficient shallow water wave equation

2019 ◽  
Vol 94 ◽  
pp. 112-119 ◽  
Author(s):  
Xiangpeng Xin ◽  
Linlin Zhang ◽  
Yarong Xia ◽  
Hanze Liu
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Wave ◽  
Variable Coefficient ◽  
Nonlocal Symmetries ◽  
Shallow Water Wave

Nonlocal symmetries and the nth finite symmetry transformation or AKNS system

2018 ◽  
Vol 32 (27) ◽  
pp. 1850332
Author(s):  
Xiazhi Hao ◽  
Yinping Liu ◽  
Xiaoyan Tang ◽  
Zhibin Li ◽  
Wen-Xiu Ma
Keyword(s):  
Exact Solutions ◽  
Symmetry Transformation ◽  
Original System ◽  
Point Symmetry ◽  
Auxiliary Variables ◽  
Nonlocal Symmetry ◽  
Nonlocal Symmetries ◽  
Akns System ◽  
Lie Point Symmetry ◽  
Physical Phenomena

In this paper, by introduction of pseudopotentials, the nonlocal symmetry is obtained for the Ablowitz–Kaup–Newell–Segur system, which is used to describe many physical phenomena in different applications. Together with some auxiliary variables, this kind of nonlocal symmetry can be localized to Lie point symmetry and the corresponding once finite symmetry transformation is calculated for both the original system and the prolonged system. Furthermore, the nth finite symmetry transformation represented in terms of determinant and exact solutions are derived.

(2+1)-dimensional (M+N)-component AKNS system: Painlevé integrability, infinitely many symmetries, similarity reductions and exact solutions

2002 ◽  
Vol 43 (8) ◽  
pp. 4078-4109 ◽  
Author(s):  
Sen-yue Lou ◽  
Chun-li Chen ◽  
Xiao-yan Tang
Keyword(s):  
Exact Solutions ◽  
Akns System ◽  
Similarity Reductions

scholarly journals Nonlocal symmetries, exact solutions and conservation laws of the coupled Hirota equations

2016 ◽  
Vol 55 ◽  
pp. 63-71 ◽  
Author(s):  
Xiangpeng Xin ◽  
Yutang Liu ◽  
Xiqiang Liu
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Nonlocal Symmetries ◽  
Hirota Equations

Exact solutions of the variable coefficient kdV and sg type equations

1998 ◽  
Vol 13 (1) ◽  
pp. 25-30 ◽  
Author(s):  
Liu Xiqiang
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient

scholarly journals Group classification and exact solutions of variable-coefficient generalized Burgers equations with linear damping

2014 ◽  
Vol 243 ◽  
pp. 232-244 ◽  
Author(s):  
Oleksandr A. Pocheketa ◽  
Roman O. Popovych ◽  
Olena O. Vaneeva
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Group Classification ◽  
Burgers Equations ◽  
Linear Damping

scholarly journals Symmetry Analysis, Bäcklund Transformations, and Interaction Solutions for an AB Modified KdV System

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Man Jia
Keyword(s):  
Symmetry Reduction ◽  
Symmetry Analysis ◽  
Bäcklund Transformations ◽  
Cnoidal Waves ◽  
Nonlocal Symmetries ◽  
Interaction Solutions ◽  
Backlund Transformations ◽  
Akns System ◽  
Finite Transformation ◽  
Truncated Painlevé Expansion

An AB modified KdV (AB-mKdV) system which can be used to describe two-place event is studied in this manuscript. Because the AB-mKdV system is considered as a special reduction of the famous AKNS system, the properties of the AKNS system are first revealed by using symmetry analysis. The nonlocal symmetries related to truncated Painlevé expansion, the finite transformation, and the symmetry reduction solutions of the AKNS system are presented. The corresponding Bäcklund transformations and the interaction solutions of the AB-mKdV system are constructed based on the special reduction. The results demonstrate that the AB-mKdV system possesses many kinds of interaction solutions, such as the interactions between kink and soliton and kink and cnoidal waves. The soliton can be changed from bright to dark during propagation.

Exact Solutions for a Nonisospectral and Variable-Coefficient KdV Equation

2005 ◽  
Vol 43 (6) ◽  
pp. 961-964 ◽  
Author(s):  
Deng Shu-Fang
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Kdv Equation

Exact Solutions of the General Variable Coefficient Kdv-Burgers Equation

2020 ◽  
Vol 09 (03) ◽  
pp. 277-284
Author(s):  
萍 张
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Burgers Equation
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