Completely integrable model of classical field theory with nontrivial particle interaction in two-dimensional space-time

Budagov, A. S.

doi:10.1007/bf01375607

Cited by 5 publications

(4 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…is a completely integrable model of classical field theory with nontrivial particle interaction [11]. This system is equivalent [11] to the compatibility condition (3.1) for systems (3.3), where l = r = 1,…”

Section: Example 2 the Modified Nonlinear Schrödinger Equation (Mnse)mentioning

confidence: 99%

“…This system is equivalent [11] to the compatibility condition (3.1) for systems (3.3), where l = r = 1,…”

Section: Example 2 the Modified Nonlinear Schrödinger Equation (Mnse)mentioning

confidence: 99%

“…Let also the parameter matrices satisfy relations (3.4) and (3.43) and det S 0 0 = 0. Then the transformed matrix functionsũ andṽ given by (3.44) satisfy the same equations (3.40) and (3.41) It is important that matrices Y −1 andṽ in [11] have the real-valued entries.…”

Section: Example 2 the Modified Nonlinear Schrödinger Equation (Mnse)mentioning

confidence: 99%

See 2 more Smart Citations

Generalized Bäcklund–Darboux Transformation: Spectral Propertiesand Nonlinear Equations

Sakhnovich¹

2001

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

Section: Example 2 the Modified Nonlinear Schrödinger Equation (Mnse)mentioning

confidence: 99%

“…This system is equivalent [11] to the compatibility condition (3.1) for systems (3.3), where l = r = 1,…”

Section: Example 2 the Modified Nonlinear Schrödinger Equation (Mnse)mentioning

confidence: 99%

See 1 more Smart Citation

Generalized Bäcklund–Darboux Transformation: Spectral Propertiesand Nonlinear Equations

Sakhnovich¹

2001

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

“…There are several other generalisations of the scalar sine-Gordon equation in the literature. For example, the well-known Budagov-Takhtajan system [17][18][19] is different from (1) if n > 1. It admits soliton decays which are not possible for equation (1).…”

Section: Introductionmentioning

confidence: 99%

Darboux Transformation for the Vector Sine-Gordon Equation and Integrable Equations on a Sphere

2016

View full text Add to dashboard Cite

We propose a method for construction of Darboux transformations, which is a new development of the dressing method for Lax operators invariant under a reduction group. We apply the method to the vector sine-Gordon equation and derive its Bäcklund transformations. We show that there is a new Lax operator canonically associated with our Darboux transformation resulting an evolutionary differential-difference system on a sphere. The latter is a generalised symmetry for the chain of Bäcklund transformations. Using the re-factorisation approach and the Bianchi permutability of the Darboux transformations, we derive new vector Yang-Baxter map and integrable discrete vector sineGordon equation on a sphere.Mathematics Subject Classification. 35Q51, 37K10, 37K35, 39A14.

show abstract

Poisson structure of the matrix sine-Gordon model

Bogolyubov¹,

Budagov²

1988

J Math Sci

View full text Add to dashboard Cite

Completely integrable model of classical field theory with nontrivial particle interaction in two-dimensional space-time

Cited by 5 publications

References 7 publications

Generalized Bäcklund–Darboux Transformation: Spectral Propertiesand Nonlinear Equations

Generalized Bäcklund–Darboux Transformation: Spectral Propertiesand Nonlinear Equations

Darboux Transformation for the Vector Sine-Gordon Equation and Integrable Equations on a Sphere

Poisson structure of the matrix sine-Gordon model

Contact Info

Product

Resources

About