This article is cited in 1 paper

Noncommutative generalization and quasi-Gramian solutions of the Hirota equation

H.  Wajahat  A. Riaz

School of Science, China University of Mining and Technology, Beijing, China

Abstract: The nonlinear Schrödinger (NLS) and modified Korteweg–de Vries (mKdV) equations can be combined to form an integrable equation known as the Hirota equation. In this paper, we investigate a noncommutative generalization of the Hirota equation by establishing the zero-curvature condition, identifying the Lax pair, and using the covariance strategy to find the binary Darboux transformation (DT) and the Darboux transformation (DT) for the noncommutative Hirota equation. We also construct the quasi-Gramian solutions. First-order single- and double-peaked solutions in noncommutative contexts are also presented.

Keywords: noncommutative integrable system, Darboux transformation, binary Darboux transformation, soliton.

Received: 07.08.2022
Revised: 15.09.2022

DOI: 10.4213/tmf10347

 English version: Theoretical and Mathematical Physics, 2023, 214:2, 194–206

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