J. Chen, D.E. Pelinovsky, and J. Upsal
Modulational instability of periodic standing waves in the derivative NLS equation
Journal of Nonlinear Science 31 (2021) 58 (32 pages)
Abstract:
We consider the periodic standing waves in the derivative nonlinear Schrodinger
(DNLS) equation arising in plasma physics. By using a newly developed algebraic method
with two eigenvalues, we classify all periodic standing waves in terms of eight eigenvalues of
the Kaup-Newell spectral problem located at the end points of the spectral bands outside
the real line. The analytical work is complemented with the numerical approximation of
the spectral bands, this enables us to fully characterize the modulational instability of the
periodic standing waves in the DNLS equation.
Keywords:
derivative nonlinear Schrodinger equation, periodic standing waves, Floquet spectrum,
modulational instability, algebraic method.