Heat Polynomials, Umbral Correspondence and Burgers Equations

Details Heat Polynomials, Umbral Correspondence and Burgers Equations Heat Polynomials, Umbral Correspondence and Burgers Equations

2006-10-31

arxiv.org/abs/nlin/0610076v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

We show that the umbral correspondence between differential equations can be achieved by means of a suitable transformation preserving the algebraic structure of the problems. We present the general properties of these transformations, derive explicit examples and discuss them in the case of the App\`{e}l and Sheffer polynomial families. We apply these transformations to non-linear equations, and discuss how the relevant solutions should be interpreted.

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