Canonical Backlund transformations and new solutions of some field equations

1990 ◽  
Vol 23 (17) ◽  
pp. L877-L880
Author(s):  
Wenhua Hai
Keyword(s):  
Bäcklund Transformations ◽  
Field Equations ◽  
Backlund Transformations

scholarly journals Similarity solutions for the Wheeler–DeWitt equation in $$f\left( R\right) $$-cosmology

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Quantum Cosmology ◽  
Classical Limit ◽  
Functional Form ◽  
Similarity Solutions ◽  
Bäcklund Transformations ◽  
Field Equations ◽  
Backlund Transformations ◽  
Classical Models

AbstractIn the case of a spatially flat Friedmann–Lemaître–Robertson–Walker Universe in $$f\left( R\right) $$fR-gravity we write the Wheeler–DeWitt equation of quantum cosmology. The equation depends upon the functional form of $$f\left( R\right) $$fR. We choose to work with four specific functions of $$f\left( R\right) $$fR in which the field equations for the classical models are integrable and solvable through quadratures. For these models we determine similarity solutions for the Wheeler–DeWitt equation by determining Lie–Bäcklund transformations. In addition we show how the classical limit is recovered by the similarity solutions of the Wheeler–DeWitt equation.

Bessel Functions, Recursion and a Nonlinear Field Equation

2001 ◽  
Vol 56 (9-10) ◽  
pp. 710-712
Author(s):  
Willi-Hans Steeb ◽  
Yorick Hardy ◽  
Ruedi Stoop
Keyword(s):  
Field Equation ◽  
Bessel Functions ◽  
Bäcklund Transformations ◽  
Nonlinear Field ◽  
Field Equations ◽  
Particular Solutions ◽  
Backlund Transformations ◽  
Nonlinear Field Equations

Abstract We show that particular solutions of certain nonlinear field equations can be constructed using Bäcklund transformations, recursion and Bessel functions.

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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