WTC solutions to a generalized nonlinear Schr\"odinger equation
Hideshi Yamane
TL;DR
This paper proves the convergence and analyticity of WTC solutions to a generalized nonlinear Schrödinger equation near movable singularities, extending previous formal solutions to actual solutions.
Contribution
It demonstrates the convergence and real-analytic nature of WTC solutions near singularities, providing rigorous validation for formal solutions.
Findings
WTC solutions are convergent near singularities.
Solutions are real-analytic near noncharacteristic, movable singularities.
Extends formal solutions to actual solutions with rigorous proofs.
Abstract
A generalized nonlinear Schr\"odinger equation admits WTC formal solutions as was shown by Clarkson. We show that they are convergent and determine real-analytic solutions near a noncharacteristic, movable singularity manifold.
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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Quantum Mechanics and Non-Hermitian Physics