Speciality:
01.01.03 (Mathematical physics)
Birth date:
05.08.1953
E-mail: ,
Keywords: integrable systems of theoretical and mathematical physics; theory of solitons; nonlinear partial equations; scattering theory; kinetic equations.
Subject:
The scheme of construction of the solution the two-dimensional boundary problem for the wide class of integrable nonlinear elliptical equations was proposed. The exact solutions of nonlinear equations of type: $\sin$-Gordon, $\pm \sh$-Gordon, ferromagnet of Heisenberg and elliptical version of the equation $-\sh$-Gordon was obtained and the "laws of conservation" and identities of traces was formulated. The new model of the magnet with variable magnetization was proposed and by the dressig method the exact solution was constructed. The gauge equivalence between the model of Heisenberg"s model and and elliptical version of equation $-\sh$-Gordon was prouved. It was demonstrated that in hyperbolic case the deformed model of Heisenberg"s feromagnet has the solutions of the type of spiral-logarithmic structures and by the method of Darboux Transformation on this base its soliton solutions are constructed.
Main publications:
Gutshabash E. Sh., Lipovskii V. D. Granichnaya zadacha dlya dvumernogo statsionarnogo magnetika Geizenberga.I // TMF, 1992, t. 90 (2), 259–272.
Varzugin G. G., Gutshabash E. Sh., Lipovskii V. D. Granichnaya zadacha dlya dvumernogo statsionarnogo magnetika Geizenberga.II // TMF, 1995, t. 104 (3), 513–529.
Gutshabash E. Sh., Lipovskii V. D., Nikulichev S. S. Nelineinaya sigma-model vVkrivolineinom prostranstve, kalibrovochnaya ekvivalentnost i (2+0)-mernye integriruemye uravneniya // TMF, 1998, 115 (3), 323–348.
Gutshabash E. Sh. Spiralno-logarifmicheskie struktury v ferromagnetike Geizenberga // Pisma v ZhETF, 2001, 73 (6), 317–319.
