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)
Journal	Journal of Dynamics and Differential Equations
DOIs	https://doi.org/10.1007/s10884-021-10112-3
State	Accepted/In press - 2022
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

Access to Document

10.1007/s10884-021-10112-3

Cite this

@article{61805e28893048edb33ee20cf05ca5b9,

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.",

keywords = "(Quasi)Periodic orbits, 35B10, 35B44, 35Q55, 37K10, Finite time blowup, Integrable system, Nonconservative equation, Nonlinear Schr{\"o}dinger equations",

author = "Jonathan Jaquette",

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

year = "2022",

doi = "10.1007/s10884-021-10112-3",

language = "English (US)",

journal = "Journal of Dynamics and Differential Equations",

issn = "1040-7294",

publisher = "Springer New York",

}

TY - JOUR

T1 - Quasiperiodicity and Blowup in Integrable Subsystems of Nonconservative Nonlinear Schrödinger Equations

AU - Jaquette, Jonathan

PY - 2022

Y1 - 2022

N2 - 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.

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.

KW - (Quasi)Periodic orbits

KW - 35B10

KW - 35B44

KW - 35Q55

KW - 37K10

KW - Finite time blowup

KW - Integrable system

KW - Nonconservative equation

KW - Nonlinear Schrödinger equations

UR - http://www.scopus.com/inward/record.url?scp=85123122420&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85123122420&partnerID=8YFLogxK

U2 - 10.1007/s10884-021-10112-3

DO - 10.1007/s10884-021-10112-3

M3 - Article

AN - SCOPUS:85123122420

SN - 1040-7294

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

ER -

Quasiperiodicity and Blowup in Integrable Subsystems of Nonconservative Nonlinear Schrödinger Equations

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this