Kink-inhomogeneity interaction in the sine-Gordon model

Area of Science:

• Nonlinear dynamics
• Condensed matter physics
• Soliton theory

Background:

• Sine-Gordon models describe various physical phenomena, including magnetic domain walls and charge density waves.
• Localized inhomogeneities can significantly alter the behavior of these systems.
• Understanding kink-inhomogeneity interactions is crucial for controlling and utilizing these systems.

Purpose of the Study:

• To investigate the dynamics of a sine-Gordon kink interacting with a localized potential energy barrier.
• To analyze the influence of dissipation on kink behavior near the barrier.
• To evaluate the effectiveness of low-dimensional models in describing these interactions.

Main Methods:

• Analytical and numerical simulations of the sine-Gordon equation.
• Investigation of kink motion near critical velocities for transmission and reflection.
• Analysis of stability properties at saddle points.
• Development and application of effective low-dimensional models (one and two degrees-of-freedom).

Main Results:

• In the absence of dissipation, the inhomogeneity acts as a potential barrier, with dynamics near critical velocities studied.
• Effective low-dimensional models accurately capture kink dynamics and stability at saddle points.
• In dissipative systems, a stable kink exists near the barrier below a threshold current.
• A two-degree-of-freedom model shows higher efficiency in capturing kink motion details compared to a one-degree-of-freedom model.

Conclusions:

• Localized inhomogeneities significantly influence sine-Gordon kink dynamics, creating potential barriers.
• Effective low-dimensional models provide accurate descriptions of kink-inhomogeneity interactions, particularly in the presence of dissipation.
• The choice of model dimensionality impacts the accuracy and efficiency of capturing complex kink behaviors.