On the construction of recursion operator and algebra of symmetries for field and lattice systems

Błaszak, Maciej

doi:10.1016/s0034-4877(01)80061-6

Cited by 17 publications

(29 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Among others, the authors illustrated the method by applying it to finite-field reductions of the KP hierarchy. In [19] the method was applied to the reductions of the modified KP hierarchy as well as to the lattice systems. Our further considerations are based on the scheme from [10] and [19].…”

Section: Recursion Operatorsmentioning

confidence: 99%

TheR-matrix approach to integrable systems on time scales

Błaszak¹,

Silindir²,

Szablikowski³

2008

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

A general unifying framework for integrable soliton-like systems on time scales is introduced. The R-matrix formalism is applied to the algebra of δdifferential operators in terms of which one can construct an infinite hierarchy of commuting vector fields. The theory is illustrated by two infinite-field integrable hierarchies on time scales which are-differential counterparts of KP and mKP. The difference counterparts of AKNS and Kaup-Broer soliton systems are constructed as related finite-field restrictions.

show abstract

Section: Recursion Operatorsmentioning

confidence: 99%

TheR-matrix approach to integrable systems on time scales

Błaszak¹,

Silindir²,

Szablikowski³

2008

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

show abstract

“…If the Lax representation of an evolutionary equation is known, an amazingly simple approach to construct a recursion operator was proposed in [17] and later applied for lattice equations [7]. This idea can also be used for Lax pairs that are invariant under a reduction group [45,20,10].…”

Section: From the Lax Representation To The Recursion Operatormentioning

confidence: 99%

Recursion and Hamiltonian operators for integrable nonabelian difference equations

Casati,

Wang

2019

Preprint

View full text Add to dashboard Cite

In this paper, we carry out the algebraic study of integrable differential-difference equations whose field variables take values in an associative (but not commutative) algebra. We adapt the Hamiltonian formalism to nonabelian difference Laurent polynomials and describe how to obtain a recursion operator from the Lax representation of an integrable nonabelian differential-difference system. As an application, we propose a novel family of integrable equations: the nonabelian Narita-Itoh-Bogoyavlensky lattice, for which we construct their recursion operators and Hamiltonian operators and prove the locality of infinitely many commuting symmetries generated from their highly nonlocal recursion operators. Finally, we discuss the nonabelian version of several integrable difference systems, including the relativistic Toda chain and Ablowitz-Ladik lattice.

show abstract

“…If the Lax representation of an evolutionary equation is known, an amazingly simple approach to construct a recursion operator was proposed in [25] and later applied for lattice equations [26]. This idea can be used for Lax pairs that are invariant under the reduction groups [20].…”

Section: Construction Of Recursion Operators From a Lax Representationmentioning

confidence: 99%

Recursion Operator of the Narita–Itoh–Bogoyavlensky Lattice

Wang

2012

Stud Appl Math

View full text Add to dashboard Cite

show abstract

On the construction of recursion operator and algebra of symmetries for field and lattice systems

Abstract: In the paper, developing the idea of V.Sokolov et all. (J.Math.Phys. 40 (1999) 6473) we construct recursion operators and hereditary algebra of symmetries for many field and lattice systems.

Cited by 17 publications

References 12 publications

TheR-matrix approach to integrable systems on time scales

TheR-matrix approach to integrable systems on time scales

Recursion and Hamiltonian operators for integrable nonabelian difference equations

Recursion Operator of the Narita–Itoh–Bogoyavlensky Lattice

Contact Info

Product

Resources

About