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Quasiperiodicity and blowup in integrable subsystems of nonconservative nonlinear Schrödinger equations
Jonathan Jaquette
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In this paper, we study the dynamics of a class of nonlinear Schr\"odinger equation i uₜ = △u + uᵖ for x ∈𝕋ᵈ. 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 L² norm.
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