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Master symmetries for differential-difference equations of the Volterra type. (English) Zbl 1194.35485

Summary: It is demonstrated that in the case of integrable differential-difference equations similar to the well-known Volterra equation (unlike the Korteweg-de Vries and nonlinear Schrödinger equations) there are many instances in which local master symmetries can be found. Those master symmetries are new interesting examples of local evolution chains explicitly depending on the time and discrete variable and integrable in a special sense. The examples are constructed by a direct and elementary approach which enables one to get new integrable equations, using Miura type transformations.

MSC:

35R10 Partial functional-differential equations
35A10 Cauchy-Kovalevskaya theorems
35Q99 Partial differential equations of mathematical physics and other areas of application
39A12 Discrete version of topics in analysis
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References:

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