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The Kundu–Eckhaus equation and its discretizations

Decio Levi1,2 and Christian Scimiterna1

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In this paper we show that the complex Burgers and the Kundu–Eckhaus equations are related by a Miura transformation. We use this relation to discretize the Kundu–Eckhaus equation.


PACS

02.30.Jr Partial differential equations

05.45.Yv Solitons

MSC

35Q51 Solitons (See also 37K40)

35Q55 NLS-like (nonlinear Schrödinger) equations (See also 37K10)

35Q53 KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.) (See also 37K10)

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 46 (20 November 2009)

Received 30 April 2009, in final form 22 September 2009

Published 22 October 2009



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