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Effective integrable dynamics for some nonlinear wave equation
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Effective integrable dynamics for some nonlinear wave equation
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We consider the following degenerate half wave equation on the one dimensional torus $$\quad i\partial_t u-|D|u=|u|^2u, \; u(0,\cdot)=u_0. $$ We show that, on a large time interval, the solution may be approximated by the solution of a completely integrable system-- the cubic Szeg\"o equation. As a consequence, we prove an instability result for large $H^s$ norms of solutions of this wave equation.
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Cited by 1 Pith paper
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A superintegrable quantum field theory
The quantum cubic Szegő equation exhibits integer spectra for its Hamiltonian and conserved hierarchies, indicating superintegrability beyond ordinary quantum integrability.
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