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The Cauchy Problem for the Defocusing Nonlinear Schrödinger Equation with a Loaded Term

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Abstract

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 \(\frac {\pi }{2} \) is the period (or antiperiod) of the initial function then \(\frac {\pi }{2} \) is the period (antiperiod) of the solution of the Cauchy problem problem with respect to \(x\).

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  1. Samarkand State University, Samarkand, 140104, Uzbekistan

    U. B. Muminov & A. B. Khasanov

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  1. U. B. Muminov
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Muminov, U.B., Khasanov, A.B. The Cauchy Problem for the Defocusing Nonlinear Schrödinger Equation with a Loaded Term. Sib. Adv. Math. 32, 277–298 (2022). https://doi.org/10.1134/S1055134422040046

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