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arXiv · 2108.00307

Quasiperiodicity and blowup in integrable subsystems of nonconservative nonlinear Schr\"odinger equations

Jonathan Jaquette
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Abstract

In this paper, we study the dynamics of a class of nonlinear Schr\"odinger equation $ i u_t = \triangle u + u^p $ for $ x \in \mathbb{T}^d$. 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 $L^2$ norm.

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Jonathan Jaquette. 2021-07-31. Quasiperiodicity and blowup in integrable subsystems of nonconservative nonlinear Schr\"odinger equations. https://arxiv.org/abs/2108.00307

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