Geodesic
Noncommutative generalization and quasi-Gramian solutions of the~Hirota equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 2, pp. 224-238

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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, binary Darboux transformation
Mots-clés : Darboux transformation, soliton. 
@article{TMF_2023_214_2_a3,
     author = {H. Wajahat A. Riaz},
     title = {Noncommutative generalization and {quasi-Gramian} solutions of {the~Hirota} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {224--238},
     publisher = {mathdoc},
     volume = {214},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_214_2_a3/}
}
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H. Wajahat A. Riaz. Noncommutative generalization and quasi-Gramian solutions of the~Hirota equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 2, pp. 224-238. http://geodesic.mathdoc.fr/item/TMF_2023_214_2_a3/