IJAM: Volume 37, No. 4 (2024)

DOI: 10.12732/ijam.v37i4.2

EXACT SOLUTIONS FOR NONLINEAR PDES

VIA HERMITE POLYNOMIALS

C. Cesarano 1, R. Garra 2,§, F. Maltese 3

1 Section of Mathematics

International Telematic University Uninettuno

Corso Vittorio Emanuele II, 39, 00186 Roma, ITALY

2 Section of Mathematics

International Telematic University Uninettuno

Corso Vittorio Emanuele II, 39, 00186 Roma, ITALY

3 I.I.S. Donato Bramante, Rome, ITALY

Abstract. In this note we construct exact solutions for nonlinear partial differential equations by means of Hermite polynomials. In particular, we consider generalized Burgers equations, that can be linearized by means of a Cole-Hopf-type transform. We show that it is possible to construct an interesting particular solution by using Hermite polynomials. We also consider a class of non-linear equations admitting isochronous solutions. The main aim is to show that Hermite polynomials can be used to construct exact solutions for a wide class of nonlinear integro-differential equations including nonlinear fractional equations.

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How to cite this paper?
DOI: 10.12732/ijam.v37i4.2
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2024
Volume: 37
Issue: 4

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