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- Title
Gain of regularity for a coupled system of generalized nonlinear Schrödinger equations.
- Authors
Mollisaca, Raul Nina; Cortés, Mauricio Sepúlveda; Asem, Rodrigo Véjar; Villagran, Octavio Vera
- Abstract
In this paper, we study the smoothness properties of solutions to a onedimensional coupled nonlinear Schrödinger system equations that describe some physical phenomena such as propagation of polarized laser beams in birefringent Kerr medium in nonlinear optics. We show that the equations dispersive nature leads to a gain in regularity for the solution. In particular, if the initial datum (u0, v0) possesses certain regularity and sufficient decay as |x| → ∞, then the solution (u(t), v(t)) will be smoother than (u0, v0) for 0 < t ≤ T, where T is the existence time of the solution.
- Subjects
NONLINEAR Schrodinger equation; SCHRODINGER equation; NONLINEAR equations; NONLINEAR optical materials; NONLINEAR systems; PHENOMENOLOGICAL theory (Physics)
- Publication
Mathematical Methods in the Applied Sciences, 2024, Vol 47, Issue 7, p5618
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9882