Geodesic
Classification of solutions of the~generalized mixed nonlinear Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 3, pp. 469-490

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We construct a generalized Darboux transformation for a generalized mixed nonlinear Schrödinger equation and consider a complete reduction classification of parameters and eigenfunctions of the two-, three-, and four-fold generalized Darboux transformations. According to these different types of reductions, several solutions of the generalized mixed nonlinear Schrödinger equation are found, including a soliton, a quasirational soliton, and a periodic soliton. Finally, a classification corresponding to these reductions is given.
Keywords: generalized mixed nonlinear Schrödinger equation, generalized Darboux transformation
Mots-clés : soliton solution. 
@article{TMF_2022_211_3_a5,
     author = {Deqin Qiu and Yongshuai Zhang},
     title = {Classification of solutions of the~generalized mixed nonlinear {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {469--490},
     publisher = {mathdoc},
     volume = {211},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_211_3_a5/}
}
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Deqin Qiu; Yongshuai Zhang. Classification of solutions of the~generalized mixed nonlinear Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 3, pp. 469-490. http://geodesic.mathdoc.fr/item/TMF_2022_211_3_a5/