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Gain of regularity for a coupled system of generalized nonlinear Schrödinger equations
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  • Mauricio Sepúlveda Cortés,
  • Raul Nina Mollisaca,
  • Rodrigo Véjar Asem,
  • Octavio Vera Villagran
Mauricio Sepúlveda Cortés
Universidad de Concepcion

Corresponding Author:[email protected]

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Raul Nina Mollisaca
Universidad de Tarapaca
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Rodrigo Véjar Asem
Universidad de La Serena
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Octavio Vera Villagran
Universidad de Tarapaca
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In this paper we study the smoothness properties of solutions to a one-dimensional coupled nonlinear Schrödinger system equations that describes 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 data ( u 0 , v 0 ) possesses certain regularity and sufficient decay as | x|→∞ , then the solution ( u( t) , v( t)) will be smoother than ( u 0 , v 0 ) for 0 ≤ T where T is the existence time of the solution.
12 Jan 2023Submitted to Mathematical Methods in the Applied Sciences
12 Jan 2023Assigned to Editor
12 Jan 2023Submission Checks Completed
18 Jan 2023Review(s) Completed, Editorial Evaluation Pending
21 Jan 2023Reviewer(s) Assigned