University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Periodic and double periodic waves in NLS: existence and stability

Periodic and double periodic waves in NLS: existence and stability

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HYD2 - Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves

I will explain how to compute the instability rates for the double-periodic solutions to the cubic NLS (nonlinear Schrödinger) equation by using the Lax linear equations. The wave function modulus of the double periodic solutions is periodic both in space and time coordinates; such solutions generalize the standing periodic waves which have the time-independent and space-periodic wave function modulus. Similar to other waves in the NLS equation, the double-periodic solutions are spectrally unstable and this instability is related to the bands of the Lax spectrum outside the imaginary axis. A simple numerical method is used to compute the unstable spectrum and to compare the instability rates of the double-periodic solutions with those of the standing periodic waves.

This talk is part of the Isaac Newton Institute Seminar Series series.

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