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The Cauchy problem for the generalized hyperbolic Novikov-Veselov equation | | V. A. Yurov
; A. V. Yurov
; | | Date: |
21 Sep 2015 | | 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
$ ext{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 $frac{d^{n-1} z}{d xi^{n-1}} = xi z$. | | Source: | arXiv, 1509.6078 | | Services: | Forum | Review | PDF | Favorites | |
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