Hiroshima Mathematical Journal

Analytic smoothing effect for system of nonlinear Schrödinger equations with general mass resonance

Takayoshi Ogawa and Takuya Sato

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Abstract

We prove the analytic smoothing e¤ect for solutions to the system of nonlinear Schrödinger equations under the gauge invariant nonlinearities. This result extends the known result due to Hoshino [Nonlinear Differential Equations Appl. 24 (2017), Art. 62]. Under rapidly decaying condition on the initial data, the solution shows a smoothing effect and is real analytic with respect to the space variable. Our theorem covers not only the case for the gauge invariant setting but also multiple component case with higher power nonlinearity up to the fifth order.

Article information

Source
Hiroshima Math. J., Volume 50, Number 1 (2020), 73-84.

Dates
Received: 19 January 2019
Revised: 21 October 2019
First available in Project Euclid: 7 March 2020

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1583550016

Digital Object Identifier
doi:10.32917/hmj/1583550016

Mathematical Reviews number (MathSciNet)
MR4074380

Zentralblatt MATH identifier
07197871

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]

Keywords
nonlinear Schrödinger equation nalytic smoothing effect gauge invariance

Citation

Ogawa, Takayoshi; Sato, Takuya. Analytic smoothing effect for system of nonlinear Schrödinger equations with general mass resonance. Hiroshima Math. J. 50 (2020), no. 1, 73--84. doi:10.32917/hmj/1583550016. https://projecteuclid.org/euclid.hmj/1583550016


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