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

Author

Listed:
  • Paz Albares

    (Departamento de Física Fundamental, Universidad de Salamanca, 37008 Salamanca, Spain
    Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK)

  • Pilar G. Estévez

    (Departamento de Física Fundamental, Universidad de Salamanca, 37008 Salamanca, Spain)

Abstract

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.

Suggested Citation

  • Paz Albares & Pilar G. Estévez, 2023. "A Comprehensive Study of the Complex mKdV Equation through the Singular Manifold Method," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:859-:d:1061238
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