BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:A.B. Borisov\, D.V. Dolgikh DTSTART:20221027T110000Z DTEND:20221027T120000Z DTSTAMP:20260423T021319Z UID:mmandim/45 DESCRIPTION:Title: Integration of the equations of the Heisenberg model (2D) and the chiral SU(2) models by differential geometry methods\nby A.B. Borisov\, D.V. Dolgikh as part of Mathematical models and integration methods\n\n\nAbstra ct\nIn the report\, to integrate the two-dimensional Heisenberg equation a nd the three-dimensional chiral SU(2) model\, the differential-geometric m ethod of integration is used\, the essence of which is as follows. First\, we perform the hodograph transformation\, i.e. change the role of depende nt and independent coordinates. Unlike the standard hodograph transformati on\, we do not just introduce derivatives of the old coordinates with resp ect to new ones\, but define through these derivatives new fields associat ed with the components of the metric tensor that appears when the hodograp h transformation is performed. Since the original independent coordinates were Euclidean\, the curvature tensor in terms of the introduced metric mu st vanish. Ultimately\, we obtain a self-consistent system of equations fo r calculating the components of the metric tensor. In this case\, the equa tions guaranteeing the curvature tensor to vanish turn out to be the main ones\, and the system of nonlinear equations of the models is their reduct ion. The solutions of the constructed equations make it possible to write the solutions of the original models in the form of implicit functions. It is important that the differential-geometric method of model integration\ , based on the embedding of a non-linear partial differential equation in a certain differential relation in Euclidean space\, makes it possible to analyze a wide variety of spatial structures\, the study of which by other methods is extremely difficult. The solutions found in the chiral SU(2) m odel describe three-dimensional configurations containing\, in particular\ , spatial vortices\, sources\, non-localized textures\, and structures wit h a mapping degree equal to one\, similar to topological solitons. In the Heisenberg model we find a vortex strip (a limited vortex region in a plan e). Many of the obtained solutions depend on arbitrary functions.\n LOCATION:https://researchseminars.org/talk/mmandim/45/ END:VEVENT END:VCALENDAR