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Khamitova, Raisa
Publications (10 of 13) Show all publications
Ibragimov, N., Khamitova, R., Avdonina, E. D. & Galiakberova, L. R. (2015). Conservation laws and solutions of a quantum drift-diffusion model for semiconductors. International Journal of Non-Linear Mechanics, 77, 69-73
Open this publication in new window or tab >>Conservation laws and solutions of a quantum drift-diffusion model for semiconductors
2015 (English)In: International Journal of Non-Linear Mechanics, ISSN 0020-7462, E-ISSN 1878-5638, Vol. 77, p. 69-73Article in journal (Refereed) Published
Abstract [en]

A non-linear system of partial differential equations describing a quantum drift-diffusion model for semiconductor devices is investigated by methods of group analysis. An infinite number of conservation laws associated with symmetries of the model are found. These conservation laws are used for representing the system of equations under consideration in the conservation form. Exact solutions provided by the method of conservation laws are discussed. These solutions are different from invariant solutions. (C) 2015 Published by Elsevier Ltd.

Keywords
Quantum semiconductor; Drift-diffusion model; Non-linear self-adjointness; Conservation laws; Exact solutions
National Category
Mathematics
Identifiers
urn:nbn:se:bth-11171 (URN)10.1016/j.ijnonlinmec.2015.07.010 (DOI)000364797600007 ()
Available from: 2015-12-11 Created: 2015-12-11 Last updated: 2017-12-01Bibliographically approved
Ibragimov, N., Khamitova, R., Avdonina, E. D. & Galiakberova, L. (2015). Group analysis of the drift–diffusion model for quantum semiconductors. Communications in nonlinear science & numerical simulation, 20(1), 74-78
Open this publication in new window or tab >>Group analysis of the drift–diffusion model for quantum semiconductors
2015 (English)In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 20, no 1, p. 74-78Article in journal (Refereed) Published
Abstract [en]

In the present paper a quantum drift–diffusion model describing semi-conductor devices is considered. New conservation laws for the model are computed and used to construct exact solutions.

Place, publisher, year, edition, pages
Elsevier, 2015
Keywords
Quantum semiconductor, quantum drift–diffusion model, group analysis, nonlinear self-adjointness, conservation laws, exact solutions
National Category
Mathematics Mathematical Analysis
Identifiers
urn:nbn:se:bth-6325 (URN)10.1016/j.cnsns.2014.05.020 (DOI)000341356700008 ()oai:bth.se:forskinfo0BA5C8D508543030C1257DA90045D563 (Local ID)oai:bth.se:forskinfo0BA5C8D508543030C1257DA90045D563 (Archive number)oai:bth.se:forskinfo0BA5C8D508543030C1257DA90045D563 (OAI)
Note

http://www.sciencedirect.com/science/article/pii/S1007570414002263

Available from: 2015-05-26 Created: 2014-12-09 Last updated: 2017-12-04Bibliographically approved
Ibragimov, N. H. & Khamitova, R. (2013). Conservation Laws in Thomas’s Model of Ion Exchange in a Heterogeneous Solution. Discontinuity, Nonlinearity and Complexity, 2(2)
Open this publication in new window or tab >>Conservation Laws in Thomas’s Model of Ion Exchange in a Heterogeneous Solution
2013 (English)In: Discontinuity, Nonlinearity and Complexity, ISSN 2164-6376, Vol. 2, no 2Article in journal (Refereed) Published
Abstract [en]

Physically significant question on calculation of conservation laws of the Thomas equation is investigated. It is demonstrated that the Thomas equation is nonlinearly self-adjoint. Using this property and applying the theorem on nonlocal conservation laws the infinite set of conservation laws corresponding to the symmetries of the Thomas equation is computed. It is shown that the Noether theorem provide only one of these conservation laws.

Place, publisher, year, edition, pages
L&H Scientific Publishing, 2013
Keywords
Ion exchange, Zeolite, Thomas’s equation, Nonlinear self-adjointness, Symmetries, Conservation laws
National Category
Mathematics Mathematical Analysis
Identifiers
urn:nbn:se:bth-6977 (URN)10.5890/DNC.2013.04.004 (DOI)oai:bth.se:forskinfo7F59D71471B2DE02C1257B79003B63E0 (Local ID)oai:bth.se:forskinfo7F59D71471B2DE02C1257B79003B63E0 (Archive number)oai:bth.se:forskinfo7F59D71471B2DE02C1257B79003B63E0 (OAI)
Available from: 2013-05-30 Created: 2013-05-28 Last updated: 2017-04-03Bibliographically approved
Avdonina, E. D., Ibragimov, N. H. & Khamitova, R. (2013). Exact solutions of gasdynamic equations obtained by the method of conservation laws. Communications in nonlinear science & numerical simulation, 18
Open this publication in new window or tab >>Exact solutions of gasdynamic equations obtained by the method of conservation laws
2013 (English)In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 18Article in journal (Refereed) Published
Abstract [en]

In the present paper, the recent method of conservation laws for constructing exact solutions for systems of nonlinear partial differential equations is applied to the gasdynamic equations describing one-dimensional and three-dimensional polytropic flows. In the one-dimensional case singular solutions are constructed in closed forms. In the threedimensional case several conservation laws are used simultaneously. It is shown that the method of conservation laws leads to particular solutions different from group invariant solutions.

Place, publisher, year, edition, pages
Elsevier B.V., 2013
Keywords
Method of conservation laws, Gasdynamic equations, Singular solutions
National Category
Mathematics Mathematical Analysis
Identifiers
urn:nbn:se:bth-6992 (URN)10.1016/j.cnsns.2012.12.023 (DOI)000317411800009 ()oai:bth.se:forskinfoC95BF2A8B691EFB5C1257B6B00447ECC (Local ID)oai:bth.se:forskinfoC95BF2A8B691EFB5C1257B6B00447ECC (Archive number)oai:bth.se:forskinfoC95BF2A8B691EFB5C1257B6B00447ECC (OAI)
Available from: 2013-05-20 Created: 2013-05-14 Last updated: 2017-12-04Bibliographically approved
Ibragimov, N. H., Khamitova, R. & Cantoni, A. (2011). Self-adjointness of a generalized Camassa-Holm equation. Applied Mathematics and Computation, 218(6), 2579-2583
Open this publication in new window or tab >>Self-adjointness of a generalized Camassa-Holm equation
2011 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 218, no 6, p. 2579-2583Article in journal (Refereed) Published
Abstract [en]

It is well known that the Camassa-Holm equation possesses numerous remarkable properties characteristic for KdV type equations. In this paper we show that it shares one more property with the KdV equation. Namely, it is shown in [1,2] that the KdV and the modified KdV equations are self-adjoint. Starting from the generalization [3] of the Camassa-Holm equation [4], we prove that the Camassa-Holm equation is self-adjoint. This property is important, e.g. for constructing conservation laws associated with symmetries of the equation in question. Accordingly, we construct conservation laws for the generalized Camassa-Holm equation using its symmetries.

Place, publisher, year, edition, pages
Elsevier, 2011
Keywords
Camassa-Holm equation, Conservation laws, Quasi self-adjointness
National Category
Mathematics
Identifiers
urn:nbn:se:bth-7381 (URN)10.1016/j.amc.2011.07.074 (DOI)000296278800020 ()oai:bth.se:forskinfo26624310AEF85400C1257979002F654B (Local ID)oai:bth.se:forskinfo26624310AEF85400C1257979002F654B (Archive number)oai:bth.se:forskinfo26624310AEF85400C1257979002F654B (OAI)
Available from: 2012-09-18 Created: 2012-01-02 Last updated: 2017-12-04Bibliographically approved
Khamitova, R. (2009). Symmetries and conservation laws. (Doctoral dissertation). Växjö: Växjö university press
Open this publication in new window or tab >>Symmetries and conservation laws
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Symmetrier och konserveringslagar
Abstract [en]

Conservation laws play an important role in science. The aim of this thesis is to provide an overview and develop new methods for constructing conservation laws using Lie group theory. The derivation of conservation laws for invariant variational problems is based on Noether’s theorem. It is shown that the use of Lie-Bäcklund transformation groups allows one to reduce the number of basic conserved quantities for differential equations obtained by Noether’s theorem and construct a basis of conservation laws. Several examples on constructing a basis for some well-known equations are provided. Moreover, this approach allows one to obtain new conservation laws even for equations without Lagrangians. A formal Lagrangian can be introduced and used for computing nonlocal conservation laws. For self-adjoint or quasi-self-adjoint equations nonlocal conservation laws can be transformed into local conservation laws. One of the fields of applications of this approach is electromagnetic theory, namely, nonlocal conservation laws are obtained for the generalized Maxwell-Dirac equations. The theory is also applied to the nonlinear magma equation and its nonlocal conservation laws are computed.

Place, publisher, year, edition, pages
Växjö: Växjö university press, 2009. p. 90 pages
Series
Acta Wexionensia, ISSN 1404-4307 ; 170
Keywords
Conservation law, Noether’s theorem, Lie group analysis, Lie-Bäcklund transformations, basis of conservation laws, formal Lagrangian, self-adjoint equation, quasi-self-adjoint equation, nonlocal conservation law
National Category
Mathematics Mathematical Analysis
Identifiers
urn:nbn:se:bth-00437 (URN)oai:bth.se:forskinfoD2A098F807334F13C125758D0037C63F (Local ID)978-91-7636-650-9 (ISBN)oai:bth.se:forskinfoD2A098F807334F13C125758D0037C63F (Archive number)oai:bth.se:forskinfoD2A098F807334F13C125758D0037C63F (OAI)
Available from: 2012-09-18 Created: 2009-04-03 Last updated: 2019-04-02Bibliographically approved
Khamitova, R. (2009). Symmetries and Nonlocal Conservation Laws of the General Magma Equation. Communications in nonlinear science & numerical simulation, 14(11), 3754-3769
Open this publication in new window or tab >>Symmetries and Nonlocal Conservation Laws of the General Magma Equation
2009 (English)In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 14, no 11, p. 3754-3769Article in journal (Refereed) Published
Abstract [en]

In this paper the general magma equation modelling a melt flow in the Earth's mantle is discussed. Applying the new theorem on nonlocal conservation laws [Ibragimov NH. A new conservation theorem. J Math Anal Appl 2007;333(1):311-28] and using the symmetries of the model equation nonlocal conservation laws are computed. In accordance with Ibragimov [Ibragimov NH. Quasi-self-adjoint differential equations. Preprint in Archives of ALGA, vol. 4, BTH, Karlskrona, Sweden: Alga Publications; 2007. p. 55-60, ISSN: 1652-4934] it is shown that the general magma equation is quasi-self-adjoint for arbitrary m and n and self-adjoint for n = -m. These important properties are used for deriving local conservation laws. © 2008 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
Elsevier BV, 2009
Keywords
magma equation, nonlocal conservation laws, quasi-self-adjointness, self-adjointness
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:bth-8320 (URN)10.1016/j.cnsns.2008.08.009 (DOI)000266896800008 ()oai:bth.se:forskinfo5F6FAF8EB0660F3CC1257515002EB096 (Local ID)oai:bth.se:forskinfo5F6FAF8EB0660F3CC1257515002EB096 (Archive number)oai:bth.se:forskinfo5F6FAF8EB0660F3CC1257515002EB096 (OAI)
Available from: 2012-09-18 Created: 2008-12-04 Last updated: 2017-12-04Bibliographically approved
Khamitova, R. (2008). Self-Adjointness and Quasi-Self-Adjointness of the Magma Equation. In: : . Paper presented at 2nd Conference on Non-linear science and complexity: session MOGRAN XII. Porto, Portugal
Open this publication in new window or tab >>Self-Adjointness and Quasi-Self-Adjointness of the Magma Equation
2008 (English)Conference paper, Oral presentation only (Refereed)
Abstract [en]

A recent theorem on nonlocal conservation laws is applied to a magma equation modelling a melt migration through the Earth´s mantle. It is shown that the equation in question is quasi-self-adjoint. The self-adjoint equations are singled out. Nonlocal and local conservation densities are obtained using the symmetries of the magma equation.

Place, publisher, year, edition, pages
Porto, Portugal: , 2008
Keywords
conservation laws, self-adjointness, quasi-self-adjointness, magma equation, Lie group analysis
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:bth-8492 (URN)oai:bth.se:forskinfoAEFFEC61ED6457AAC12574A5003321C0 (Local ID)oai:bth.se:forskinfoAEFFEC61ED6457AAC12574A5003321C0 (Archive number)oai:bth.se:forskinfoAEFFEC61ED6457AAC12574A5003321C0 (OAI)
Conference
2nd Conference on Non-linear science and complexity: session MOGRAN XII
Available from: 2012-09-18 Created: 2008-08-14 Last updated: 2015-09-28Bibliographically approved
Ibragimov, N. H., Khamitova, R. & Thidé, B. (2007). Conservation laws for symmetrised electromagnetic equations with a dual Ohm's law. In: : . Paper presented at International conference MOGRAN 11, Karlskrona. Karlskrona, Sweden
Open this publication in new window or tab >>Conservation laws for symmetrised electromagnetic equations with a dual Ohm's law
2007 (English)Conference paper, Oral presentation only (Refereed)
Abstract [en]

In all areas of physics, conservation laws are essential since they allow us to draw conclusions of our physical system under study in an indirect but efficient way. Electrodynamics, in terms of the standard Maxwell electromagnetic equations for fields in vacuum, exhibit a rich set of symmetries to which conserved quantities are associated. We have derived conservation laws for Dirac's symmetric version of the Maxwell-Lorentz microscopic equations, allowing magnetic charges and magnetic currents, where the latter, just as electric currents, are assumed to be described by a linear relationship between the field and the current, i.e. an Ohm's law. We find that when we use the method of Ibragimov to construct the conservation laws, they will contain two new adjoint vector fields which fulfil Maxwell-like equations. In particular, we obtain conservation laws for the electromagnetic field which are nonlocal in time.

Place, publisher, year, edition, pages
Karlskrona, Sweden: , 2007
Keywords
Conservation laws, Maxwell electromagnetic equations for fields in vacuum
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:bth-8718 (URN)oai:bth.se:forskinfo635747B58EC2FE42C12573C900334809 (Local ID)oai:bth.se:forskinfo635747B58EC2FE42C12573C900334809 (Archive number)oai:bth.se:forskinfo635747B58EC2FE42C12573C900334809 (OAI)
Conference
International conference MOGRAN 11, Karlskrona
Available from: 2012-09-18 Created: 2008-01-07 Last updated: 2015-09-28Bibliographically approved
Ibragimov, N. H., Khamitova, R. & Thidé, B. (2007). Conservation laws for the Maxwell-Dirac equations with dual Ohm's law. Journal of Mathematical Physics, 48(5)
Open this publication in new window or tab >>Conservation laws for the Maxwell-Dirac equations with dual Ohm's law
2007 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 48, no 5Article in journal (Refereed) Published
Abstract [en]

Using a general theorem on conservation laws for arbitrary differential equations proved by Ibragimov [J. Math. Anal. Appl. 333, 311-320 (2007)], we have derived conservation laws for Dirac's symmetrized Maxwell-Lorentz equations under the assumption that both the electric and magnetic charges obey linear conductivity laws (dual Ohm's law). We find that this linear system allows for conservation laws which are nonlocal in time. (c) 2007 American Institute of Physics.

Place, publisher, year, edition, pages
MELVILLE: AMER INST PHYSICS, 2007
Keywords
conservation laws, Maxwell equations, differential equations, electric charge
National Category
Mathematics
Identifiers
urn:nbn:se:bth-8198 (URN)10.1063/1.2735822 (DOI)000246892400060 ()oai:bth.se:forskinfo44B2490363645CDDC12575B00020D269 (Local ID)oai:bth.se:forskinfo44B2490363645CDDC12575B00020D269 (Archive number)oai:bth.se:forskinfo44B2490363645CDDC12575B00020D269 (OAI)
Available from: 2012-09-18 Created: 2009-05-08 Last updated: 2017-12-04Bibliographically approved
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