On a damped Szegö equation (with an appendix in collaboration with Christian Klein). (English) Zbl 1448.35022
Summary: We investigate how damping the lowest Fourier mode modifies the dynamics of the cubic Szegö equation. We show that there is a nonempty open subset of initial data generating trajectories with high Sobolev norms tending to infinity. In addition, we give a complete picture of this phenomenon on a reduced phase space of dimension 6. An appendix is devoted to numerical simulations supporting the generalization of this picture to more general initial data.
MSC:
| 35B15 | Almost and pseudo-almost periodic solutions to PDEs |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 47B35 | Toeplitz operators, Hankel operators, Wiener-Hopf operators |
| 37K15 | Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems |
Keywords:
cubic Szegö equation; integrable system; damped equation; Hankel operator; spectral analysisReferences:
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