The classical problem of the Josephson tunnel junction of arbitrary (but finite) barrier length in the presence of external parallel magnetic fields and transport currents was solved analytically [2, 3, 4]. Exact analytical expressions for the complete set of Josephson vortices (topological solitons of the static sine-Gordon equation) were obtained.
Exact analytical expressions for the complete set of static topological solitons in mesoscopic two-band-superconducting cylinders were derived. Their physical properties were thoroughly discussed .
Based on mathematical methods and concepts of modern quantum field theory, we proposed a new and rigorous approach to the theory of superconductivity of structurally-inhomogeneous systems .
1. S. V. Kuplevakhsky
Exact solutions of the Lawrence-Doniach model for layered superconductors.
Phys. Rev. B 63, 054508 (2001) arXiv
2. S. V. Kuplevakhsky and A. M. Glukhov
Static solitons of the sine-Gordon equation and equilibrium vortex structure in Josephson junctions.
Phys. Rev. B 73, 024513 (2006) arXiv
3. S. V. Kuplevakhsky and A. M. Glukhov
Exact analytical solution of the problem of current-carrying states of the Josephson junction in external magnetic fields.
Phys. Rev. B 76, 174515 (2007)
4. S. V. Kuplevakhsky and A. M. Glukhov
Exact analytical solution of a classical problem of the Josephson tunnel junction .
Low Temp. Phys. 36, 1012 (2010)
5. S. V. Kuplevakhsky, A.N. Omelyanchouk, and Y.S. Yerin
Soliton states in mesoscopic two-band-superconducting cylinders.
Low Temp. Phys. 37, 667
6. S. V. Kuplevakhsky
Higgs mechanism in superconducting structures.
Low Temp. Phys. 43, 329 (2017)