Quasiperiodicity and Blowup in Integrable Subsystems of Nonconservative Nonlinear Schrödinger Equations

Jonathan Jaquette

doi:10.1007/s10884-021-10112-3

Quasiperiodicity and Blowup in Integrable Subsystems of Nonconservative Nonlinear Schrödinger Equations

Jonathan Jaquette

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we study the dynamics of a class of nonlinear Schrödinger equation iu_t=▵u+u^p for x∈T^d. We prove that the PDE is integrable on the space of non-negative Fourier modes, in particular that each Fourier coefficient of a solution can be explicitly solved by quadrature. Within this subspace we demonstrate a large class of (quasi)periodic solutions all with the same frequency, as well as solutions which blowup in finite time in the L² norm.

Original language	English (US)
Pages (from-to)	1-25
Number of pages	25
Journal	Journal of Dynamics and Differential Equations
Volume	36
Issue number	1
DOIs	https://doi.org/10.1007/s10884-021-10112-3
State	Published - Mar 2024
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis

Keywords

(Quasi)Periodic orbits
35B10
35B44
35Q55
37K10
Finite time blowup
Integrable system
Nonconservative equation
Nonlinear Schrödinger equations

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10.1007/s10884-021-10112-3

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title = "Quasiperiodicity and Blowup in Integrable Subsystems of Nonconservative Nonlinear Schr{\"o}dinger Equations",

abstract = "In this paper, we study the dynamics of a class of nonlinear Schr{\"o}dinger equation iut=▵u+up for x∈Td. We prove that the PDE is integrable on the space of non-negative Fourier modes, in particular that each Fourier coefficient of a solution can be explicitly solved by quadrature. Within this subspace we demonstrate a large class of (quasi)periodic solutions all with the same frequency, as well as solutions which blowup in finite time in the L2 norm.",

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note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021.",

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AU - Jaquette, Jonathan

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AB - In this paper, we study the dynamics of a class of nonlinear Schrödinger equation iut=▵u+up for x∈Td. We prove that the PDE is integrable on the space of non-negative Fourier modes, in particular that each Fourier coefficient of a solution can be explicitly solved by quadrature. Within this subspace we demonstrate a large class of (quasi)periodic solutions all with the same frequency, as well as solutions which blowup in finite time in the L2 norm.

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KW - 35Q55

KW - 37K10

KW - Finite time blowup

KW - Integrable system

KW - Nonconservative equation

KW - Nonlinear Schrödinger equations

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Quasiperiodicity and Blowup in Integrable Subsystems of Nonconservative Nonlinear Schrödinger Equations

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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