An impacton solution for the vortex filament
A new way of construction of exact solutions describing the shape and the dynamics of vortex filaments is described. The new method is based on application of a binary Darboux transformation to the solutions of the nonlinear Schrödinger equation. A new type of solutions is constructed: the impacton. The explicit form of the curvature and torsion of corresponding vortex filament are calculated.
1. Валландер С. В. Лекции по гидроаэромеханике. Л.,...
A surprising tale of long-periodic spin oscillations in the synthetic antiferromagnets: some exact solutions
... collisions between the magnetic domains of different spin orientations ( and ). The resulting model comprised of a system of nonlinear differential equations is closely examined, after which we propose a simple analytical method of construction of its exact solutions. This ... ... perfectly fits the experimental data.
Yurov V. A., Yurov A. V., Morgunov R. B.
synthetic antiferromagnets, domain walls, Schrödinger equation, degenerate hypergeometric equation
1+1-Dimensional Yang — Mills Equations and Mass via Quasiclassical Correction to Action
Two-dimensional Yang — Mills models in a pseudo-euclidean space are considered from a point of view of a class of nonlinear Klein — Gordon — Fock equations. It is shown that the Nahm reduction does not work, another, novel choice is proposed and investigated. A quasiclassical ... ... Proper Time in Classical and Quantum // Phys. Zeit. d. Sowjetunion. 1937. Vol. 12. P. 404—425.
19. Its A. R., Matveev V. B. Schrödinger Operators with the Finite-Band Spectrum and the N-soliton Solutions of the Korteweg — de Vries Equation // Teor....