Geodesic
One-phase and two-phase solutions of the focusing nonlinear Schrodinger equation
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2020), pp. 18-34

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A periodic boundary value problem for the focusing nonlinear Schrodinger equation is considered. This version of the equation has applications in nonlinear optics. The existence of single-phase solutions with the structure of traveling waves is shown. For such solutions, the question of their stability is considered. Three other types of single-phase solutions are found. Asymptotic formulas are obtained for these solutions. It is also shown that these solutions generate three types of already two-phase solutions of the main boundary value problem for the focusing Schrodinger equation. For this, the principle of self-similarity is used. Some results can be applied to the defocusing version of the nonlinear Schrodinger equation.
Keywords: focusing nonlinear Schrodinger equation, periodic value boundary problem, principle of self-similarity, one-phase, two-phase solutions. 
@article{VTPMK_2020_2_a1,
     author = {A. N. Kulikov and D. A. Kulikov},
     title = {One-phase and two-phase solutions of the focusing nonlinear {Schrodinger} equation},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {18--34},
     publisher = {mathdoc},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2020_2_a1/}
}
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A. N. Kulikov; D. A. Kulikov. One-phase and two-phase solutions of the focusing nonlinear Schrodinger equation. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2020), pp. 18-34. http://geodesic.mathdoc.fr/item/VTPMK_2020_2_a1/