Geodesic
The Cauchy problem for the defocusing nonlinear Schr\"odinger equation with a loaded term
Matematičeskie trudy, Tome 25 (2022) no. 1, pp. 102-133

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The method of inverse spectral problems is applied for integrating the defocusing nonlinear Scrödinger (DNS) equation with loaded terms in the class of infinite-gap periodic functions. We describe the evolution of the spectral data for a periodic Dirac operator whose coefficient is a solution to the DNS equation with loaded terms. We prove the following assertions. (1) It the initial function is real-valued, $\pi$-periodic, and analytic then the solution of the Cauchy problem for the DNS equation with loaded terms is a real-valued analytic function in $x$. (2) If $\pi/2$ is the period (or antiperiod) of the initial function then $\pi/2$ is the period (antiperiod) of the solution of the Cauchy problem problem with respect to $x$. 
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     author = {U. B. Muminov and A. B. Khasanov},
     title = {The {Cauchy} problem for the defocusing nonlinear {Schr\"odinger} equation with a loaded term},
     journal = {Matemati\v{c}eskie trudy},
     pages = {102--133},
     publisher = {mathdoc},
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     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2022_25_1_a4/}
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U. B. Muminov; A. B. Khasanov. The Cauchy problem for the defocusing nonlinear Schr\"odinger equation with a loaded term. Matematičeskie trudy, Tome 25 (2022) no. 1, pp. 102-133. http://geodesic.mathdoc.fr/item/MT_2022_25_1_a4/