Nonlinear Schrödinger equation and frequency saturation
Copyright policy )Nonlinear Schrödinger equation and frequency saturation
We propose an approach that permits to avoid instability phenomena for the nonlinear Schrodinger equations. We show that by approximating the solution in a suitable way, relying on a frequency cut-off, global well-posedness is obtained in any Sobolev space with nonnegative regularity. The error between the exact solution and its approximation can be measured according to the regularity of the exact solution, with different accuracy according to the cases considered.
Comment: 15 pages: appendix added
35Q55, 35B30, 35A01, Mathematics - Analysis of PDEs, 35B65, well-posedness, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], nonlinear Schrödinger equation, approximation, 35B45
35Q55, 35B30, 35A01, Mathematics - Analysis of PDEs, 35B65, well-posedness, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], nonlinear Schrödinger equation, approximation, 35B45
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