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
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| 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$, where $\ell</math> stands for the linearization and <math>\ell^*</math> stands for its adjoint. Many examples of computations for evolutionary and non-evolutionary equations will be provided. | | abstract = It is generally agreed that a system of (non-linear) differential equations is said to be integrable if there exists an infinite sequence of commuting generalized symmetries. Such a sequence can be generated through differential operators like recursion operators, (commuting pairs of) Hamiltonian operators or symplectic operators. In this talk a new method for finding such operators will be presented. It amounts at computing the operators as generalized symmetries of a system of (nonlinear) DEs which is obtained from the initial system of PDEs <math>F=0</math> by adding the equations <math>\ell_F(q)=0</math> or <math>\ell_F^*(p)=0$, where $\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 | ||
}} | }} | ||
Revision as of 16:18, 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 stands for the linearization and stands for its adjoint. Many examples of computations for evolutionary and non-evolutionary equations will be provided.
