# 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} }

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.

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