D.E. Pelinovsky
Instability of double-periodic solutions in the nonlinear Schrodinger equation
Frontiers in Physics 9 (2021) 599146 (10 pages)
Abstract:
It is shown how to compute the instability rates for the double-periodic solutions to the
cubic NLS (nonlinear Schrodinger) 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 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.
Keywords:
nonlinear Schrodinger equation, double-periodic solutions, Lax spectrum, modulational instability.