The Kundu--Eckhaus equation and its discretizations
Decio Levi, Christian Scimiterna
TL;DR
This paper explores the relationship between the complex Burgers and Kundu--Eckhaus equations via a Miura transformation and introduces a discretization method for the Kundu--Eckhaus equation based on this relation.
Contribution
It establishes a connection between the complex Burgers and Kundu--Eckhaus equations and provides a novel discretization approach for the latter.
Findings
The complex Burgers and Kundu--Eckhaus equations are related by a Miura transformation.
A new discretization scheme for the Kundu--Eckhaus equation is proposed.
The discretization leverages the established relation to preserve key properties.
Abstract
In this article 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.
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