Exact solutions of the inhomogeneous nonlinear Schrödinger equation through supersymmetric potentials

• URL: http://arxiv.org/abs/2511.18186v1
• Date: Sat, 22 Nov 2025 20:43:06 GMT
• Title: Exact solutions of the inhomogeneous nonlinear Schrödinger equation through supersymmetric potentials
• Authors: David J. Fernández C., O. Pavón-Torres,
• Abstract summary: We derive exact stationary solutions of the inhomogeneous nonlinear Schrdinger equation (INLSE)<n>This is possible due to the connection between the INLSE and the nonlinear Schrdinger equation (NLSE), which can be established from a treatment based on Lie point symmetries.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: By employing supersymmetric quantum mechanics, we present a general algorithm to construct supersymmetric partner potentials and hence derive exact stationary solutions of the inhomogeneous nonlinear Schrödinger equation (INLSE). This is possible due to the connection between the INLSE and the nonlinear Schrödinger equation (NLSE), which can be established from a treatment based on Lie point symmetries and is related with Schrödinger equation, under certain conditions. As an illustrative example, we construct exact solutions for the INLSE through a Pösch-Teller potential with a single bound state.

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