Quasiperiodicity and blowup in integrable subsystems of nonconservative nonlinear Schrödinger equations
Abstract
In this paper, we study the dynamics of a class of nonlinear Schrödinger 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 nonnegative 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2108.00307
 Bibcode:
 2021arXiv210800307J
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Dynamical Systems;
 35B10;
 35B44;
 35Q55;
 37K10
 EPrint:
 24 pages, 1 figure