Geodesic
Integration of a~defocusing nonlinear Schr\"odinger equation with additional terms
Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 1, pp. 84-104

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The inverse spectral problem method is used to integrate the nonlinear Schrödinger equation with some additional terms in the class of infinite-gap periodic functions. We reveal the evolution of spectral data for a periodic Dirac operator whose coefficients solve the Cauchy problem for a nonlinear Schrödinger equation with some additional terms. Several examples are given to illustrate the algorithm described in the paper.
Keywords: nonlinear Schrödinger equation, Dirac operator, spectral data, inverse spectral problem, system of Dubrovin equations, trace formulas. 
@article{TMF_2022_211_1_a5,
     author = {U. B. Muminov and A. B. Khasanov},
     title = {Integration of a~defocusing nonlinear {Schr\"odinger} equation with additional terms},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {84--104},
     publisher = {mathdoc},
     volume = {211},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_211_1_a5/}
}
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U. B. Muminov; A. B. Khasanov. Integration of a~defocusing nonlinear Schr\"odinger equation with additional terms. Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 1, pp. 84-104. http://geodesic.mathdoc.fr/item/TMF_2022_211_1_a5/