The Novikov--Veselov equation and the inverse scattering method: II. Computation

Lassas, Matti; Mueller, Jennifer L.; Siltanen, Samuli; Stahel, Andreas (2012). The Novikov--Veselov equation and the inverse scattering method: II. Computation Nonlinearity, 25(6), pp. 1799-1818. IOP 10.1088/0951-7715/25/6/1799

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The Novikov–Veselov (NV) equation is a (2 + 1)-dimensional nonlinear evolution equation generalizing the (1 + 1)-dimensional Korteweg–deVries equation. The inverse scattering method (ISM) is applied for numerical solution of the NV equation. It is the first time the ISM is used as a computational tool for computing evolutions of a (2 + 1)-dimensional integrable system. In addition, a semi-implicit method is given for the numerical solution of the NV equation using finite differences in the spatial variables, Crank–Nicolson in time, and fast Fourier transforms for the auxiliary equation. Evolutions of initial data satisfying the hypotheses of part I of this paper are computed by the two methods and are observed to coincide with significant accuracy.

Item Type:	Journal Article (Original Article)
Division/Institute:	School of Engineering and Computer Science > Institute for Human Centered Engineering (HUCE) > HUCE / Laboratory for Sensors
Name:	Lassas, Matti; Mueller, Jennifer L.; Siltanen, Samuli and Stahel, Andreas
ISSN:	1361-6544
Publisher:	IOP
Language:	English
Submitter:	Andreas Stahel
Date Deposited:	18 Nov 2020 14:49
Last Modified:	18 Nov 2020 14:49
Publisher DOI:	10.1088/0951-7715/25/6/1799
ARBOR DOI:	10.24451/arbor.13032
URI:	https://arbor.bfh.ch/id/eprint/13032