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Keywords = Moutard symmetry

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17 pages, 2465 KiB  
Article
The Cauchy Problem for the Generalized Hyperbolic Novikov–Veselov Equation via the Moutard Symmetries
by Alla A. Yurova, Artyom V. Yurov and Valerian A. Yurov
Symmetry 2020, 12(12), 2113; https://doi.org/10.3390/sym12122113 - 19 Dec 2020
Cited by 2 | Viewed by 2386
Abstract
We begin by introducing a new procedure for construction of the exact solutions to Cauchy problem of the real-valued (hyperbolic) Novikov–Veselov equation which is based on the Moutard symmetry. The procedure shown therein utilizes the well-known Airy function Ai(ξ) which [...] Read more.
We begin by introducing a new procedure for construction of the exact solutions to Cauchy problem of the real-valued (hyperbolic) Novikov–Veselov equation which is based on the Moutard symmetry. The procedure shown therein utilizes the well-known Airy function Ai(ξ) which in turn serves as a solution to the ordinary differential equation d2zdξ2=ξz. In the second part of the article we show that the aforementioned procedure can also work for the n-th order generalizations of the Novikov–Veselov equation, provided that one replaces the Airy function with the appropriate solution of the ordinary differential equation dn1zdξn1=ξz. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2020)
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