Quasiperiodicity and Blowup in Integrable Subsystems of Nonconservative Nonlinear Schrödinger Equations

  title={Quasiperiodicity and Blowup in Integrable Subsystems of Nonconservative Nonlinear Schr{\"o}dinger Equations},
  author={Jonathan Jaquette},
  journal={Journal of Dynamics and Differential Equations},
  • 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. 
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