Coupled Modes Approach to Non-Linear Dispersive Wave. II. Effect of Dissipation on Recurrence

Dissipative effects on the recurrence of an initial waveform are examined by analysing numerically the K-dV equation with a dissipation term. Two different wave dissipations are considered; frequency dependent and independent wave dampings. The recurrence in a dissipative system is imperfect as well as in a non-dissipative system. The spectrum at the recurrence point sensitively changes depending on the dissipation coefficient and the amplitude of the second harmonic increases with the dissipation, if the wave damping is not large. The recurrence length increases with the dissipation, but the mechanism of the increase depends on the structure of the dissipation term.