Towards Lax Formulation of Integrable Hierarchies of Topological Type
| Autor: | van de Leur, Johannes, Carlet, Guido, Shadrin, Sergey, Posthuma, Hessel, Sub Fundamental Mathematics, Sub Algebra,Geometry&Mathem. Logic begr., Fundamental mathematics |
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| Přispěvatelé: | Algebra, Geometry & Mathematical Physics (KDV, FNWI), Sub Fundamental Mathematics, Sub Algebra,Geometry&Mathem. Logic begr., Fundamental mathematics |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Hierarchy
Integrable system Infinitesimal FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Partition function (mathematics) Fundamental lemma Topology symbols.namesake Quadratic equation Nonlinear Sciences::Exactly Solvable and Integrable Systems symbols Hamiltonian (quantum mechanics) Korteweg–de Vries equation Mathematics::Symplectic Geometry Mathematical Physics Mathematics |
| Zdroj: | Communications in Mathematical Physics, 326(3), 815-849. Springer New York Communications in Mathematical Physics, 326, 815. Springer New York |
| ISSN: | 0010-3616 |
| DOI: | 10.1007/s00220-014-1898-z |
| Popis: | To each partition function of cohomological field theory one can associate an Hamiltonian integrable hierarchy of topological type. The Givental group acts on such partition functions and consequently on the associated integrable hierarchies. We consider the Hirota and Lax formulations of the deformation of the hierarchy of N copies of KdV obtained by an infinitesimal action of the Givental group. By first deforming the Hirota quadratic equations and then applying a fundamental lemma to express it in terms of pseudo-differential operators, we show that such deformed hierarchy admits an explicit Lax formulation. We then compare the deformed Hamiltonians obtained from the Lax equations with the analogous formulas obtained in [1, 2], to find that they agree. We finally comment on the possibility of extending the Hirota and Lax formulation on the whole orbit of the Givental group action. Comment: 36 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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