Gardner's deformation of the Krasil'shchik—Kersten system

7th International Workshop: Group Analysis of Differential Equations and Integrable Systems

Kiselev, Arthemy V.^1 ; Krutov, Andrey O.^2

Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, AK Groningen

9700, Netherlands^1

Department of Higher Mathematics, Ivanovo State Power University, Rabfakovskaya str. 34, Ivanovo

153003, Russia^2

关键词: Classical problems;    Completely integrable systems;    Curvature representation;    Infinite dimensional;    Integrals of motion;    Nonlocal variables;    Partial differential equations (PDE);    Recurrence relations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/621/1/012007/pdf
DOI  :  10.1088/1742-6596/621/1/012007

来源: IOP

【 摘 要 】

The classical problem of construction of Gardner's deformations for infinite-dimensional completely integrable systems of evolutionary partial differential equations (PDE) amounts essentially to finding the recurrence relations between the integrals of motion. Using the correspondence between the zero-curvature representations and Gardner deformations for PDE, we construct a Gardner's deformation for the Krasil'shchik-Kersten system. For this, we introduce the new nonlocal variables in such a way that the rules to differentiate them are consistent by virtue of the equations at hand and second, the full system of Krasil'shchik-Kersten's equations and the new rules contains the Korteweg-de Vries equation and classical Gardner's deformation for it.