Cylindrical Korteweg-de Vries solitons in the vortex dynamics of an ultraclean type-II superconductor

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Abstract
A theory for weakly nonlinear and dispersive wave propagation in an Abrikosov vortex lattice in a type-II superconductor of cylindrical symmetry is presented. A continuum treatment of the London equation with vortex term is used, allowing nonlocal lattice elasticity. Vortex inertia is included, but pinning is ignored. A dynamical regime is derived where the cylindrical Korteweg-de Vries (CKdV) equation governs the evolution of the first-order field corrections. Fundamental properties of the CKdV equation are briefly recalled and a prototypical soliton solution is given and discussed. Dynamical system analogies are mentioned.