Abstract:
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.
Keywords:nonlinear Schrödinger equation of negative order, Dirac operator, spectral
data, Dubrovin system of equations, trace formulas.
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