Spectral solutions to the Korteweg-de-Vries and nonlinear Schrodinger equations

Chellappan, Vinita and Gopalakrishnan, S and Mani, V (2015) Spectral solutions to the Korteweg-de-Vries and nonlinear Schrodinger equations. In: CHAOS SOLITONS & FRACTALS, 81 (A). pp. 150-161.

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Abstract

In this paper, we present the solutions of 1-D and 2-D non-linear partial differential equations with initial conditions. We approach the solutions in time domain using two methods. We first solve the equations using Fourier spectral approximation in the spatial domain and secondly we compare the results with the approximation in the spatial domain using orthogonal functions such as Legendre or Chebyshev polynomials as their basis functions. The advantages and the applicability of the two different methods for different types of problems are brought out by considering 1-D and 2-D nonlinear partial differential equations namely the Korteweg-de-Vries and nonlinear Schrodinger equation with different potential function. (C) 2015 Elsevier Ltd. All rights reserved.

Item Type:	Journal Article
Publication:	CHAOS SOLITONS & FRACTALS
Publisher:	PERGAMON-ELSEVIER SCIENCE LTD
Additional Information:	Copy right for this article belongs to the PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
Keywords:	Spectral methods; Polynomial approximation; Solitons; Partial differential equations
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	14 Jan 2016 07:34
Last Modified:	14 Jan 2016 07:34
URI:	http://eprints.iisc.ac.in/id/eprint/53042

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