A Comprehensive Study of the Complex mKdV Equation through the Singular Manifold Method

In this paper, we introduce a modification of the Singular Manifold Method in order to derive the associated spectral problem for a generalization of the complex version of the modified Korteweg–de Vries equation. This modification yields the right Lax pair and allows us to implement binary Darboux...

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Bibliographic Details
Published in:Mathematics
Main Authors: Paz Albares, Pilar G. Estévez
Format: Article
Language:English
Published: MDPI AG 2023-02-01
Subjects:
integrability
complex mKdV equation
Singular Manifold Method
Lax pair
Darboux transformations
soliton solutions
Online Access:https://www.mdpi.com/2227-7390/11/4/859
Description
Summary:In this paper, we introduce a modification of the Singular Manifold Method in order to derive the associated spectral problem for a generalization of the complex version of the modified Korteweg–de Vries equation. This modification yields the right Lax pair and allows us to implement binary Darboux transformations, which can be used to construct an iterative method to obtain exact solutions.
ISSN:2227-7390

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