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.
Biography
Graduated from Faculty of Mathematics and Mechanics of Leningrad State University (LSU) in 1975 (department of physical mechanics). Ph.D. thesis was defended in 1994. A list of my works contains more than 30 titles.
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.
E. Sh. Gutshabash, “Legendre transformation in Born–Infeld models, Monge–Ampere equation and exact solutions”, Zap. Nauchn. Sem. POMI, 520 (2023), 151–161
2017
2.
E. Sh. Gutshabash, P. P. Kulish, “New exact solutions of the Born–Infeld model”, Zap. Nauchn. Sem. POMI, 465 (2017), 135–146; J. Math. Sci. (N. Y.), 238:6 (2019), 854–861
E. Sh. Gutshabash, “Nonlinear sigma model, Zakharov–Shabat method, and new exact forms of the minimal surfaces in ${\mathbb R}^3$”, Pis'ma v Zh. Èksper. Teoret. Fiz., 99:12 (2014), 827–831; JETP Letters, 99:12 (2014), 715–719
E. Sh. Gutshabash, “Moutard transformation and its application to some physical problems. I. The case of two independent variables”, Zap. Nauchn. Sem. POMI, 398 (2012), 100–124; J. Math. Sci. (N. Y.), 192:1 (2013), 57–69
E. Sh. Gutshabash, “On equation of minimal surface in $\mathbb R^3$: different representations, properties of exact solutions, conservation laws”, Zap. Nauchn. Sem. POMI, 374 (2010), 121–135; J. Math. Sci. (N. Y.), 168:6 (2010), 829–836
E. Sh. Gutshabash, P. P. Kulish, “Discrete symmetries, Darboux transformation, and exact solutions of the Wess–Zumino–Novikov–Witten model”, Zap. Nauchn. Sem. POMI, 360 (2008), 139–152; J. Math. Sci. (N. Y.), 158:6 (2009), 845–852
E. Sh. Gutshabash, “On canonical variables for integrable models of magnets”, Zap. Nauchn. Sem. POMI, 347 (2007), 117–143; J. Math. Sci. (N. Y.), 151:2 (2008), 2865–2879
2006
9.
E. Sh. Gutshabash, “Hydrodynamical vortice on the plain”, Zap. Nauchn. Sem. POMI, 335 (2006), 119–133; J. Math. Sci. (N. Y.), 143:1 (2007), 2765–2772
E. Sh. Gutshabash, “Darboux transformation for the nonstationary Schrödinger equation”, Zap. Nauchn. Sem. POMI, 317 (2004), 94–104; J. Math. Sci. (N. Y.), 136:1 (2006), 3580–3585
E. Sh. Gutshabash, “Generalized Darboux transform in the Ishimori magnet model on the background of spiral structures”, Pis'ma v Zh. Èksper. Teoret. Fiz., 78:11 (2003), 1257–1; JETP Letters, 78:11 (2003), 740–744
E. Sh. Gutshabash, “Spiral-logarithmic structures in a Heisenberg ferromagnet”, Pis'ma v Zh. Èksper. Teoret. Fiz., 73:6 (2001), 316–318; JETP Letters, 73:6 (2001), 279–281
2000
14.
E. Sh. Gutshabash, “On some set of models of magnets and chiral fields: integrability, Darboux transformation and exact solutions”, Zap. Nauchn. Sem. POMI, 269 (2000), 164–179; J. Math. Sci. (N. Y.), 115:1 (2003), 1977–1985
E. Sh. Gutshabash, V. D. Lipovskii, S. S. Nikulichev, “Nonlinear $\sigma$-model in a curved space, gauge equivalence, and exact solutions of
$(2+0)$-dimensional integrable equations”, TMF, 115:3 (1998), 323–348; Theoret. and Math. Phys., 115:3 (1998), 619–638
E. Sh. Gutshabash, “Inverse scattering transform for the Coulomb's plasma with the negative temperature”, Zap. Nauchn. Sem. POMI, 251 (1998), 215–232; J. Math. Sci. (New York), 104:3 (2001), 1218–1228
1997
17.
E. Sh. Gutshabash, “The transformation of Pohlmeyer and $(2+0)$ integrable equations of statistical physics”, Zap. Nauchn. Sem. POMI, 245 (1997), 149–165; J. Math. Sci. (New York), 100:2 (2000), 2105–2115
G. G. Varzugin, E. Sh. Gutshabash, V. D. Lipovskii, “Boundary-value problem for the two-dimensional stationary Heisenberg magnet with non-trivial background. II”, TMF, 104:3 (1995), 513–529; Theoret. and Math. Phys., 104:3 (1995), 1166–1177
E. Sh. Gutshabash, “Some geometrical aspects of nonlinear $Î(Ç)$ sigmamodel in $(2+0)$ dimensions”, Zap. Nauchn. Sem. POMI, 209 (1994), 20–27; J. Math. Sci., 83:1 (1997), 11–15
1992
20.
E. Sh. Gutshabash, V. D. Lipovskii, “Boundary-value problem for two-dimensional stationary Heisenberg magnet with nontrivial background. I”, TMF, 90:2 (1992), 259–272; Theoret. and Math. Phys., 90:2 (1992), 175–184
E. Sh. Gutshabash, V. D. Lipovsky, “Exact solutions of nonlinear sigma-model in curved space and the theory of media with variable saturation magnetization”, Zap. Nauchn. Sem. POMI, 199 (1992), 71–80; J. Math. Sci., 77:2 (1995), 3063–3068
E. S. Gutshabash, V. D. Lipovskii, “Boundary-value problem for two-dimensional elliptic sine-Gordon equation and it's application to the theory of stationary Josephson effect”, Zap. Nauchn. Sem. LOMI, 180 (1990), 53–62; J. Math. Sci., 68:2 (1994), 197–201
G. G. Varzugin, E. Sh. Gutshabash, V. D. Lipovskii, “Corrigenda: “Boundary-value problem for the two-dimensional heisenberg magnetic with nontrivial background. II”
Theor. Math. Phyz., Vol. 104, № 3, pp. 1166–1177 (1995)”, TMF, 106:1 (1996), 175; Theoret. and Math. Phys., 106:1 (1996), 150
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