Construction of Bäcklund Transformations with Binary Bell Polynomials

1997 ◽  
Vol 66 (8) ◽  
pp. 2211-2213 ◽  
Author(s):  
Franklin Lambert ◽  
Johan Springael
Keyword(s):  
Bäcklund Transformations ◽  
Bell Polynomials ◽  
Backlund Transformations ◽  
Binary Bell Polynomials

Multi-soliton Collisions and Bäcklund Transformations for the (2+1)-dimensional Modified Nizhnik–Novikov–Vesselov Equations

2015 ◽  
Vol 70 (8) ◽  
pp. 629-635
Author(s):  
Xi-Yang Xie ◽  
Bo Tian ◽  
Yu-Feng Wang ◽  
Wen-Rong Sun ◽  
Ya Sun
Keyword(s):  
Acoustic Waves ◽  
Water Waves ◽  
Soliton Solutions ◽  
Bäcklund Transformations ◽  
Bell Polynomials ◽  
Ion Acoustic Waves ◽  
Backlund Transformations ◽  
Kdv Type Equations ◽  
Binary Bell Polynomials ◽  
Soliton Collisions

AbstractThe Korteweg–de Vries (KdV)-type equations can describe the shallow water waves, stratified internal waves, ion-acoustic waves, plasma physics and lattice dynamics, while the (2+1)-dimensional Nizhnik–Novikov–Vesselov equations are the isotropic extensions of KdV-type equations. In this paper, we investigate the (2+1)-dimensional modified Nizhnik–Novikov–Vesselov equations. By virtue of the binary Bell polynomials, bilinear forms, multi-soliton solutions and Bäcklund transformations are derived. Effects of some parameters on the solitons and monotonic function are graphically illustrated. We can observe the coalescence of the two solitons in their collision region, where their shapes change after the collision.

Solitons, Bäcklund transformations, Lax pair and conservation laws for the nonautonomous mKdV–sinh-Gordon equation with time-dependent coefficients

2016 ◽  
Vol 30 (03) ◽  
pp. 1650008 ◽  
Author(s):  
Lei Liu ◽  
Bo Tian ◽  
Wen-Rong Sun ◽  
Yu-Feng Wang ◽  
Yun-Po Wang
Keyword(s):  
Conservation Laws ◽  
Gordon Equation ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Time Dependent ◽  
Bäcklund Transformations ◽  
Bell Polynomials ◽  
Bilinear Forms ◽  
Bell Polynomial ◽  
Backlund Transformations

The transition phenomenon of few-cycle-pulse optical solitons from a pure modified Korteweg–de Vries (mKdV) to a pure sine-Gordon regime can be described by the nonautonomous mKdV–sinh-Gordon equation with time-dependent coefficients. Based on the Bell polynomials, Hirota method and symbolic computation, bilinear forms and soliton solutions for this equation are obtained. Bäcklund transformations (BTs) in both the binary Bell polynomial and bilinear forms are obtained. By virtue of the BTs and Ablowitz–Kaup–Newell–Segur system, Lax pair and infinitely many conservation laws for this equation are derived as well.

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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