Classical and Quantum Nonlinear Integrable System

2003 ◽  
Keyword(s):  
Integrable System ◽  
Nonlinear Integrable System

NEW JACOBI ELLIPTIC FUNCTION SOLUTIONS OF (2 +1)-DIMENSIONAL COMPLEX NONLINEAR INTEGRABLE SYSTEM

2003 ◽  
Vol 14 (03) ◽  
pp. 277-284 ◽  
Author(s):  
ZHENYA YAN
Keyword(s):  
Periodic Solutions ◽  
Integrable System ◽  
Symbolic Computation ◽  
Elliptic Function ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Jacobi Elliptic Function ◽  
Jacobian Elliptic Functions ◽  
Jacobi Elliptic Function Expansion ◽  
Nonlinear Integrable System

Recently sixteen types of doubly-periodic solutions were obtained for the new (2 +1)-dimensional complex nonlinear integrable system. In this paper with the aid of computerized symbolic computation, our extended Jacobi elliptic function expansion method is extended to this system. As a result, another eight families of Jacobian elliptic functions solutions are also found.

On the Heisenberg Supermagnet Model in (2+1)-Dimensions

2017 ◽  
Vol 72 (4) ◽  
pp. 331-337 ◽  
Author(s):  
Zhao-Wen Yan
Keyword(s):  
Integrable System ◽  
Integrable Systems ◽  
Bäcklund Transformations ◽  
Quadratic Constraints ◽  
Backlund Transformations

AbstractThe Heisenberg supermagnet model is an important supersymmetric integrable system in (1+1)-dimensions. We construct two types of the (2+1)-dimensional integrable Heisenberg supermagnet models with the quadratic constraints and investigate the integrability of the systems. In terms of the gage transformation, we derive their gage equivalent counterparts. Furthermore, we also construct new solutions of the supersymmetric integrable systems by means of the Bäcklund transformations.

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