Moving solitons in superconductors and Peyerls systems

An exact solution to the problem of moving solitons in anisotropic superconductors and in Peyerls systems is obtained by the method of reduction to the reverse problem of scattering, which has already yielded exact quiescent soliton solutions. Metals with almost plane segments of the Fermi surface are considered, and that surface is assumed to have the form of a parallelepiped. The equilibrium value of the order parameter is determined from the effective soliton action in terms of scattering parameters of the electronic subsystem and electron-proton interaction parameters, with the aid of quasi-classical Green functions integrated with respect to the energy variable. The order parameter for a single domain wall and a charged polaron is then calculated, assuming first a quiescent soliton, whereupon the surface energy of a domain well is found by a Legendre transformation of the soliton action. Complete integrability with respect to time makes it possible to obtain an exact moving soliton solution, in the absence of pinning by structural defects.