May/June 2023 The higher order nonlinear Schrödinger equation with quadratic nonlinearity on the real axis
Andrei V. Faminskii
Adv. Differential Equations 28(5/6): 413-466 (May/June 2023). DOI: 10.57262/ade028-0506-413

Abstract

The initial value problem is considered for a higher order nonlinear Schrödinger equation with quadratic nonlinearity. Results on existence and uniqueness of weak solutions are obtained. In the case of an effective at infinity additional damping large-time decay of solutions without any smallness assumptions is also established. The main difficulty of the study is the non-smooth character of the nonlinearity.

Citation

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Andrei V. Faminskii. "The higher order nonlinear Schrödinger equation with quadratic nonlinearity on the real axis." Adv. Differential Equations 28 (5/6) 413 - 466, May/June 2023. https://doi.org/10.57262/ade028-0506-413

Information

Published: May/June 2023
First available in Project Euclid: 27 February 2023

Digital Object Identifier: 10.57262/ade028-0506-413

Subjects:
Primary: 35Q31 , 76B03

Rights: Copyright © 2023 Khayyam Publishing, Inc.

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Vol.28 • No. 5/6 • May/June 2023
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