An algebraic formula for superposition and the completeness of the Bäcklund transformations of (2+1)-dimensional integrable systems

1996 ◽  
Vol 51 (6) ◽  
pp. 1200-1202 ◽  
Author(s):  
E I Ganzha ◽  
S P Tsarev
Keyword(s):  
Integrable Systems ◽  
Bäcklund Transformations ◽  
Backlund Transformations ◽  
Algebraic Formula

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.

INTEGRABLE ASPECTS OF NONCOMMUTATIVE ANTI-SELF-DUAL YANG-MILLS EQUATIONS

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2237-2238 ◽  
Author(s):  
MASASHI HAMANAKA
Keyword(s):  
Integrable Systems ◽  
Soliton Solutions ◽  
Bäcklund Transformations ◽  
Soliton Theory ◽  
Yang Mills ◽  
Backlund Transformations ◽  
Exact Soliton Solutions

We discuss extension of soliton theory and integrable systems to non-commutative (NC) spaces, focusing on integrable aspects of NC Anti-Self-Dual Yang-Mills (ASDYM) equations. We give exact soliton solutions (with both finite- and infinite-action solutions) by means of Bäcklund transformations. In the construction of NC soliton solutions, one kind of NC determinants, quasideterminants, play crucial roles. This is partially based on collaboration with C. R. Gilson and J. J. C. Nimmo (Glasgow).

scholarly journals Bäcklund transformations of the first kind associated with Monge-Ampère’s equations

1973 ◽  
Vol 51 ◽  
pp. 161-184
Author(s):  
Michihiko Matsuda
Keyword(s):  
Integrable Systems ◽  
Bäcklund Transformation ◽  
Bäcklund Transformations ◽  
Contact Transformation ◽  
Backlund Transformation ◽  
Backlund Transformations ◽  
The Given

Due to Clairin and Goursat, a Bäcklund transformation of the first kind can be associated with Monge-Ampère’s equation. We shall consider Monge-Ampère’s equation of the form s + f(x, y, z, p, q) + g(x, y, z, p, q) t = 0, where p = ∂z/∂x, q = ∂z/∂y, s = ∂2z/∂x∂y, t = ∂2z/∂y2. The following theorems will be obtained:1. The transformed equation takes on the same form s′ + f′ + g′t′ = 0 if and only if the given equation can be transformed to a Teixeira equation s + L(x, y, z, q)t + M(x, y, z, q)p + N(x, y, z, q) = 0 by a contact transformation.2. Teixeira equation s + tL + pM + N = 0 is solved by integrable systems of order n if and only if the transformed equation is solved by integrable systems of order n — 1.

scholarly journals On the Higher-Order Inhomogeneous Heisenberg Supermagnetic Models

2021 ◽  
Vol 28 (4) ◽  
pp. 345-362
Author(s):  
Rong Han ◽  
Haichao Sun ◽  
Nana Jiang ◽  
Zhaowen Yan
Keyword(s):  
Gauge Transformation ◽  
Integrable Systems ◽  
Higher Order ◽  
Nonlinear Schrödinger Equations ◽  
Bäcklund Transformations ◽  
Schrödinger Equations ◽  
Quadratic Constraints ◽  
Nonlinear Schrodinger Equations ◽  
Backlund Transformations ◽  
Fifth Order

AbstractThis paper is concerned with the construction of the fifth-order inhomogeneous Heisenberg supermagnetic models. Moreover, the Lax representations of the models are presented. By means of the gauge transformation, we establish their gauge equivalent equations with different quadratic constraints, i.e., the super and fermionic fifth-order inhomogeneous nonlinear Schrödinger equations, respectively. In addition, we investigate their Lax representations and Bäcklund transformations from which the solutions of the super integrable systems have been discussed.

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