# Quasiperiodicity and Blowup in Integrable Subsystems of Nonconservative Nonlinear Schrödinger Equations

@article{Jaquette2022QuasiperiodicityAB,
title={Quasiperiodicity and Blowup in Integrable Subsystems of Nonconservative Nonlinear Schr{\"o}dinger Equations},
author={Jonathan Jaquette},
journal={Journal of Dynamics and Differential Equations},
year={2022}
}
• Jonathan Jaquette
• Published 31 July 2021
• Mathematics
• Journal of Dynamics and Differential Equations
In this paper, we study the dynamics of a class of nonlinear Schrödinger equation iut = 4u + u for x ∈ T. We prove that the PDE is integrable on the space of non-negative Fourier coefficients, 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 L norm.
2 Citations

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## References

SHOWING 1-10 OF 37 REFERENCES

### A remark on norm inflation for nonlinear Schrödinger equations

• Nobu Kishimoto
• Mathematics
Communications on Pure & Applied Analysis
• 2019
We consider semilinear Schr\"odinger equations with nonlinearity that is a polynomial in the unknown function and its complex conjugate, on $\mathbb{R}^d$ or on the torus. Norm inflation

### QUASI-PERIODIC SOLUTIONS OF HAMILTONIAN PERTURBATIONS OF 2D LINEAR SCHRODINGER EQUATIONS

The general problem discussed here is the persistency of quasi-periodic solutions of linear or integrable equations after Hamiltonian perturbation. This subject is closely related to the well-known

### On global existence of L2 solutions for 1D periodic NLS with quadratic nonlinearity

• Mathematics
Journal of Mathematical Physics
• 2021
We study the 1D nonlinear Schrodinger equation with non-gauge invariant quadratic nonlinearity on the torus. The Cauchy problem admits trivial global dispersive solutions, which are constant with

### Invariant tori for the cubic Szegö equation

• Mathematics
• 2010
AbstractWe continue the study of the following Hamiltonian equation on the Hardy space of the circle, $$i\partial_tu=\Pi(|u|^2u),$$ where Π denotes the Szegö projector. This equation can be seen as

### Ill-posedness for the nonlinear Schrödinger equation with quadratic non-linearity in low dimensions

• Mathematics
• 2014
. We consider the ill-posedness issue for the nonlinear Schr¨odinger equation with a quadratic nonlinearity. We reﬁne the Bejenaru-Tao result by constructing an example in the following sense. There