Sine-Gordon Equation and Soliton Dynamics
Derived and simulated traveling wave and multi-soliton solutions for variable-length pendula, investigating the effects of perturbations and linking results to Josephson junction physics.
Studied a chain of pendula coupled by springs with variable lengths, deriving the Sine-Gordon equation with x-dependent parameters. Found analytical traveling wave and multi-soliton solutions, including kink, antikink, and breather waves. Conducted numerical simulations to explore how variations in pendulum length create effective potential wells or barriers, affecting soliton trapping, collisions, and oscillations. Extended the model to include perturbations such as dissipation, driving forces, and higher-order terms, demonstrating their impact on soliton behavior. Connected the findings to long Josephson junctions, interpreting pendulum length variations as spatial variations in dielectric properties, providing insight into real physical systems.
Academic Context
