Mixed Problem for a Nonlinear Schrödinger Equation of Negative Order in the Class of Periodic Infinite-Gap Functions

Аннотация

The inverse spectral problem method is applied to integrate a negative-order nonlinear Schrödinger equation in the class of periodic infinite-gap functions. The evolution of spectral data for a periodic Dirac operator whose coefficient is a solution to the negative-order nonlinear Schrödinger equation is introduced. An algorithm for deriving the Dubrovin differential equation system is proposed. The solvability of the Cauchy problem for the infinite Dubrovin differential equation system in the class of twice continuously differentiable periodic infinite-gap functions is proved. It is shown that, for sufficiently smooth initial data, there exists a global solution to the mixed problem for the negative-order nonlinear Schrödinger equation.

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DOI

10.1134/s0001434625602801

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