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Auto-Bäcklund transformations for a differential-delay equation
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Discrete Painlevé equations have, over recent years, generated much interest. One property of such equations that is considered to be particularly important is the existence of auto-Bäcklund transformations, that is, mappings between solutions of the equation in question, usually involving changes in the values of parameters appearing as coefficients. We have recently presented extensions of discrete Painlevé equations to equations involving derivatives as well as shifts in the independent variable. Here we show how auto-Bäcklund transformations can also be constructed for such differential-delay equations. We emphasise that this is the first time that an auto-Bäcklund transformation has been given for a differential-delay equation.
Title: Auto-Bäcklund transformations for a differential-delay equation
Description:
Discrete Painlevé equations have, over recent years, generated much interest.
One property of such equations that is considered to be particularly important is the existence of auto-Bäcklund transformations, that is, mappings between solutions of the equation in question, usually involving changes in the values of parameters appearing as coefficients.
We have recently presented extensions of discrete Painlevé equations to equations involving derivatives as well as shifts in the independent variable.
Here we show how auto-Bäcklund transformations can also be constructed for such differential-delay equations.
We emphasise that this is the first time that an auto-Bäcklund transformation has been given for a differential-delay equation.
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