In this paper, we study the dynamics of a class of nonlinear Schrödinger equation iut= ▵u+ up for x∈ Td. We prove that the PDE is integrable on the space of non-negative Fourier modes, 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 L2 norm.
All Science Journal Classification (ASJC) codes
- (Quasi)Periodic orbits
- Finite time blowup
- Integrable system
- Nonconservative equation
- Nonlinear Schrödinger equations