D.E. Pelinovsky, Yu.S. Kivshar, and V.V. Afanasjev
Internal modes of envelope solitons
Physica D 116, 121-142 (1998)
Abstract:
We extend the concept of internal mode to envelope solitons
and show that this mode is responsible for long-lived, weakly
damped periodic oscillations of the soliton
amplitude observed in numerical simulations. We present
analytical and numerical results for solitons of the
generalized nonlinear Schrodinger equation and analyze the
example of the cubic-quintic nonlinearity in more detail.
We obtain also analytical criteria for the existence and
bifurcations of the soliton internal mode and calculate
the rate of the radiation-induced damping of the soliton
oscillations induced by excitation of the internal mode.
Keywords:
NONLINEAR SCHRODINGER EQUATION, KINK-ANTIKINK INTERACTIONS,
SINE-GORDON MODEL, SOLITARY WAVES, IMPURITY INTERACTIONS,
INTERNAL MODES, INSTABILITY, RADIATION, EIGENVALUE PROBLEMS, ENVELOPE SOLITONS