an:00859665
Zbl 0863.35109
Krichever, I. M.
Two-dimensional algebraic-geometric operators with self-consistent potentials
EN
Funct. Anal. Appl. 28, No. 1, 21-32 (1994); translation from Funkts. Anal. Prilozh. 28, No. 1, 26-40 (1994).
00025383
1994
j
35Q75 81U40 53Z05 81T30 81Q05
exact string solutions; de Sitter spacetime; self-consistent potentials; nonlinear Schr??dinger equation
The article is concerned with the construction of exact solutions of the string equations in \((2+1)\)-dimensional de Sitter spacetime. The author notices that equations describing the problem can be related to a set of linear equations with the self-consistent potentials. Adopting the methods of the construction of exact solutions of the nonlinear Schr??dinger equation, he shows that the generalization is so effective that the general nonlinear \(\sigma\)-model equations with the string constraints can be solved. Here the construction of the solution of the nonlinear problem consists in considering the family of integrable linear problems and selecting these with potentials filfilling the self-consistency conditions.
Firstly, the method of construction of integrable potentials for the two-dimensional nonlinear Schr??dinger equation is recalled. Then the constraints for the theory parameters yielding the self-consistency conditions for the string case are analysed. Finally, the \(\Theta\)-functional formulas for the solutions of string theory for \((2+1)\)-dimensional de Sitter spacetime are derived.
A.Frydryszak (Wroc??aw)