Korteweg–de Vries equation in the vortex dynamics of an ultraclean type-II superconductor
Mark W. Coffey
DOI 10.1103/PhysRevB.52.R13122 · Physical Review B
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Abstract
A theory for weakly nonlinear and dispersive wave propagation in an Abrikosov vortex lattice in a type-II superconductor is presented. The coupled nonlinear electrodynamics of an isotropic, ultraclean superconductor is modelled. A continuum treatment of the London equation with vortex term is used. A dynamical regime is derived where the Korteweg–de Vries equation governs the evolution of the first-order field corrections. The effects of nonlocal lattice elasticity and vortex inertia are included. A prototypical soliton solution is given and discussed and a dynamical system analogy is described.
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