TY - JOUR

T1 - Nonlinear analysis of the modulational instability of a tachyonic wave train in the damped dc-driven sine-Gordon model

AU - Malomed, Boris A.

PY - 1991

Y1 - 1991

N2 - It is known that a near-linear solution (a train of densely packed kinks) of the underdamped sine-Gordon equation with a dc driving term has a region of modulational instability in the tachyonic regime, in which the trains velocity exceeds the limit velocity of the sine-Gordon model. In the present work a nonlinear analysis of this instability is developed for the slightly overcritical case. A system of coupled evolution equations for two complex amplitudes of the growing disturbances is derived, and it is demonstrated that the instability gives rise to a pair of coupled small-amplitude waves of modulation traveling along the underlying wave train. A physical implementation is proposed in terms of an I-V characteristic of a long Josephson junction described by this model. It is shown that, at the point where the instability sets in, the I-V characteristic suffers a break. A corresponding jump of the differential resistance is found.

AB - It is known that a near-linear solution (a train of densely packed kinks) of the underdamped sine-Gordon equation with a dc driving term has a region of modulational instability in the tachyonic regime, in which the trains velocity exceeds the limit velocity of the sine-Gordon model. In the present work a nonlinear analysis of this instability is developed for the slightly overcritical case. A system of coupled evolution equations for two complex amplitudes of the growing disturbances is derived, and it is demonstrated that the instability gives rise to a pair of coupled small-amplitude waves of modulation traveling along the underlying wave train. A physical implementation is proposed in terms of an I-V characteristic of a long Josephson junction described by this model. It is shown that, at the point where the instability sets in, the I-V characteristic suffers a break. A corresponding jump of the differential resistance is found.

UR - http://www.scopus.com/inward/record.url?scp=14344269662&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.43.10197

DO - 10.1103/PhysRevB.43.10197

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AN - SCOPUS:14344269662

SN - 0163-1829

VL - 43

SP - 10197

EP - 10200

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

IS - 13

ER -