The Cauchy problem for the generalized hyperbolic Novikov-Veselov equation

V. A. Yurov; A. V. Yurov

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arXiv · 1509.06078

The Cauchy problem for the generalized hyperbolic Novikov-Veselov equation

V. A. Yurov·A. V. Yurov

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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. The procedure shown therein utilizes the well-known Airy function $\text{Ai}(\xi)$ which in turn serves as a solution to the ordinary differential equation $\frac{d^2 z}{d \xi^2} = \xi z$. 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 $\frac{d^{n-1} z}{d \xi^{n-1}} = \xi z$.

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V. A. Yurov, A. V. Yurov. 2015-09-21. The Cauchy problem for the generalized hyperbolic Novikov-Veselov equation. https://arxiv.org/abs/1509.06078

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