Exploring solutions for the negative-order modified Korteweg–de Vries equation with a self-consistent source corresponding to moving eigenvalues

G. U. Urazboev^ab, I. I. Baltaeva^a, Sh. E. Atanazarova<sup>ab

a</sup> Urgench State University, Urgench, Uzbekistan
^b Khorezm Branch of the Romanovsky Institute of Mathematics, Uzbekistan Academy of Sciences, Urgench, Uzbekistan

Abstract: We focus on investigating the negative-order modified Korteweg–de Vries equation with a special source. Based on the inverse scattering transform method, we derive the temporal dependency of scattering data for the Dirac operator with moving eigenvalues. We derive the multisoliton solution to considered problem using matrix triplet method and illustrate the wave behavior of solutions in both presence and absence of a source.

Keywords: negative-order modified Korteweg–de Vries equation, inverse scattering transform, eigenvalue, potential, matrix triplet, special source, eigenvalues.

Received: 20.02.2025
Revised: 14.04.2025

DOI: 10.4213/tmf10944

 English version: Theoretical and Mathematical Physics, 2025, 225:2, 1896–1909

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