Perturbation theory for nonlinear Schrodinger equations

• URL: http://arxiv.org/abs/2206.09826v2
• Date: Mon, 22 Jul 2024 13:40:59 GMT
• Title: Perturbation theory for nonlinear Schrodinger equations
• Authors: Andrea Sacchetti,
• Abstract summary: This power series is proved to be convergent when the parameter representing the intensity of the nonlinear term is less in absolute value than a threshold value. It gives a stationary solution to the nonlinear Schrodinger equation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Treating the nonlinear term of the Gross-Pitaevskii nonlinear Schrodinger equation as a perturbation of an isolated discrete eigenvalue of the linear problem one obtains a Rayleigh-Schrodinger power series. This power series is proved to be convergent when the parameter representing the intensity of the nonlinear term is less in absolute value than a threshold value, and it gives a stationary solution to the nonlinear Schrodinger equation.

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