Krasilshchik J., Verbovetsky A., Vitolo R. On the relationship between integrability structures and higher symmetries, talk at WASCOM 2011 (Brindisi, Italy), 13-16 June 2011 (abstract): Difference between revisions
Created page with "{{MeetingTalk | speaker = Raffaele Vitolo | title = On the relationship between integrability structures and higher symmetries | abstract = It is generally agreed that a system o..." |
No edit summary |
||
| (One intermediate revision by the same user not shown) | |||
| Line 2: | Line 2: | ||
| speaker = Raffaele Vitolo | | speaker = Raffaele Vitolo | ||
| title = On the relationship between integrability structures and higher symmetries | | title = On the relationship between integrability structures and higher symmetries | ||
| abstract = It is generally agreed that a system of (non-linear) differential equations is said to be integrable if there exists an infinite sequence of commuting generalized symmetries. Such a sequence can be generated through differential operators like recursion operators, (commuting pairs of) Hamiltonian operators or symplectic operators. In this talk a new method for finding such operators will be presented. It amounts at computing the operators as generalized symmetries of a system of (nonlinear) DEs which is obtained from the initial system of PDEs <math>F=0</math> by adding the equations <math>\ell_F(q)=0</math> or <math>\ell_F^*(p)=0 | | abstract = It is generally agreed that a system of (non-linear) differential equations is said to be integrable if there exists an infinite sequence of commuting generalized symmetries. Such a sequence can be generated through differential operators like recursion operators, (commuting pairs of) Hamiltonian operators or symplectic operators. In this talk a new method for finding such operators will be presented. It amounts at computing the operators as generalized symmetries of a system of (nonlinear) DEs which is obtained from the initial system of PDEs <math>F=0</math> by adding the equations <math>\ell_F(q)=0</math> or <math>\ell_F^*(p)=0</math>, where <math>\ell</math> stands for the linearization and <math>\ell^*</math> stands for its adjoint. Many examples of computations for evolutionary and non-evolutionary equations will be provided. | ||
| slides = [[Media:Krasilshchik J., Verbovetsky A., Vitolo R. On the relationship between integrability structures and higher symmetries (presentation at WASCOM 2011, Brindisi, Italy, 12-18 June 2011).pdf]] | | slides = [[Media:Krasilshchik J., Verbovetsky A., Vitolo R. On the relationship between integrability structures and higher symmetries (presentation at WASCOM 2011, Brindisi, Italy, 12-18 June 2011).pdf|Krasilshchik J., Verbovetsky A., Vitolo R. On the relationship between integrability structures and higher symmetries (presentation at WASCOM 2011, Brindisi, Italy, 12-18 June 2011).pdf]] | ||
| references = | | references = | ||
| 79YY-MM-DD = 7988-93-86 | | 79YY-MM-DD = 7988-93-86 | ||
}} | }} | ||
Latest revision as of 16:20, 23 June 2011
Speaker: Raffaele Vitolo
Title: On the relationship between integrability structures and higher symmetries
Abstract:
It is generally agreed that a system of (non-linear) differential equations is said to be integrable if there exists an infinite sequence of commuting generalized symmetries. Such a sequence can be generated through differential operators like recursion operators, (commuting pairs of) Hamiltonian operators or symplectic operators. In this talk a new method for finding such operators will be presented. It amounts at computing the operators as generalized symmetries of a system of (nonlinear) DEs which is obtained from the initial system of PDEs by adding the equations or , where stands for the linearization and stands for its adjoint. Many examples of computations for evolutionary and non-evolutionary equations will be provided.
