论文信息 - On solutions of nonlinear Schrödinger equations with Cantor-type spectrum

On solutions of nonlinear Schrödinger equations with Cantor-type spectrum

The solvability of the Cauchy problem for the Nonlinear Nonfocusing Schrödinger equation (NNSE) with almost periodic initial data satisfying certain conditions is studied. It is shown that solutions are uniform almost periodic functions with respect to each variable. An example of initial data with Cantor-type spectrum is given. The Cauchy problem for NNSE is solved in the class of limit periodic functions which are well approximated by periodic ones.

Anne Boutet de Monvel | A. B. D. Monvel | Ira Egorova | I. Egorova

[1] P. Yuditskii,et al. Almost periodic Sturm-Liouville operators with Cantor homogeneous spectrum , 1995 .

[2] Russell Johnson,et al. The algebraic-geometric AKNS potentials , 1987, Ergodic Theory and Dynamical Systems.

[3] Iryna Egorova,et al. The Cauchy problem for the KdV equation with almost periodic initial data whose spectrum is nowhere dense , 1994 .

[4] M. Ablowitz,et al. The Periodic Cubic Schrõdinger Equation , 1981 .

[5] B. M. Levitan,et al. Inverse Sturm-Liouville Problems , 1987 .

[6] Henry P. McKean,et al. Hill’s Operator and Hyperelliptic Function Theory in the Presence of Infinitely Many Branch Points , 1976 .

[7] P. Yuditskii,et al. Almost periodic Jacobi matrices with homogeneous spectrum, infinite dimensional Jacobi inversion, and hardy spaces of character-automorphic functions , 1997 .

[8] Alexander Figotin,et al. Spectra of Random and Almost-Periodic Operators , 1991 .

[9] Sergei Petrovich Novikov,et al. NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES , 1976 .

[10] W. Craig. The trace formula for Schrödinger operators on the line , 1989 .

[11] V. Marchenko. Sturm-Liouville Operators and Applications , 1986 .

[12] M. Väth. Operators and applications , 1997 .

[13] V. Marčenko. THE PERIODIC KORTEWEG-de VRIES PROBLEM , 1974 .