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dc.creatorAcosta-Humánez P.spa
dc.creatorGiraldo H.spa
dc.creatorPiedrahita C.spa
dc.date.accessioned2017-12-19T19:36:44Z
dc.date.available2017-12-19T19:36:44Z
dc.date.created2017
dc.identifier.issn9720871
dc.identifier.urihttp://hdl.handle.net/11407/4276
dc.description.abstractThe trajectory of energy is modeled by the solution of the Eikonal equation, which can be solved by solving a Hamiltonian system. This system is amenable of treatment from the point of view of the theory of differential algebra. In particular, by Morales-Ramis theory, it is possible to analyze integrable Hamiltonian systems through the abelian structure of their variational equations. In this paper, we obtain the abelian differential Galois groups and the representation of the quiver, that allow us to obtain such abelian differential Galois groups, for some seismic models with constant Hessian of square of slowness, proposed in [20], which are equivalent to linear Hamiltonian systems with three uncoupled harmonic oscillators. © 2017 Pushpa Publishing House, Allahabad, India.eng
dc.language.isoeng
dc.publisherPushpa Publishing Housespa
dc.relation.isversionofhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85027419050&doi=10.17654%2fMS102030599&partnerID=40&md5=cbf516e16e7dfa97fbf4463dc175d5b6spa
dc.sourceScopusspa
dc.titleDifferential galois groups and representation of quivers for seismic models with constant hessian of square of slownessspa
dc.typeArticleeng
dc.rights.accessrightsinfo:eu-repo/semantics/restrictedAccess
dc.contributor.affiliationAcosta-Humánez, P., School of Basic and Biomedical Sciences, Universidad Simón Bolívar, Barranquilla, Colombiaspa
dc.contributor.affiliationGiraldo, H., Institute of Mathematics, Universidad de Antioquia, Medellín, Colombiaspa
dc.contributor.affiliationPiedrahita, C., Department of Basic Sciences, Universidad de Medellín, Medellín, Colombiaspa
dc.identifier.doi10.17654/MS102030599
dc.subject.keywordDifferential Galois theoryeng
dc.subject.keywordEikonal equationeng
dc.subject.keywordHamilton equationeng
dc.subject.keywordHelmholtz equationeng
dc.subject.keywordHigh frequency approximationeng
dc.subject.keywordMorales-Ramis theoryeng
dc.subject.keywordRay theoryeng
dc.subject.keywordRepresentations of quiverseng
dc.publisher.facultyFacultad de Ciencias Básicasspa
dc.abstractThe trajectory of energy is modeled by the solution of the Eikonal equation, which can be solved by solving a Hamiltonian system. This system is amenable of treatment from the point of view of the theory of differential algebra. In particular, by Morales-Ramis theory, it is possible to analyze integrable Hamiltonian systems through the abelian structure of their variational equations. In this paper, we obtain the abelian differential Galois groups and the representation of the quiver, that allow us to obtain such abelian differential Galois groups, for some seismic models with constant Hessian of square of slowness, proposed in [20], which are equivalent to linear Hamiltonian systems with three uncoupled harmonic oscillators. © 2017 Pushpa Publishing House, Allahabad, India.eng
dc.creator.affiliationSchool of Basic and Biomedical Sciences, Universidad Simón Bolívar, Barranquilla, Colombiaspa
dc.creator.affiliationInstitute of Mathematics, Universidad de Antioquia, Medellín, Colombiaspa
dc.creator.affiliationDepartment of Basic Sciences, Universidad de Medellín, Medellín, Colombiaspa
dc.relation.ispartofesFar East Journal of Mathematical Sciencesspa
dc.relation.ispartofesFar East Journal of Mathematical Sciences Volume 102, Issue 3, August 2017, Pages 599-623spa
dc.relation.referencesAcosta-Humánez, P., & BlAzquez-Sanz, D. (2008). Non-integrability of some hamiltonians with rational potentials. Discrete and Continuous Dynamical Systems - Series B, 10(2-3), 265-293.spa
dc.relation.referencesAcosta-Humánez, P., & Blázquez-Sanz, D. (2008). Hamiltonian system and variational equations with polynomial coefficients. Dynamic Systems and Applications, Dynamic, Atlanta, GA, 5, 6-10.spa
dc.relation.referencesAcosta-Humánez, P., & Suazo, E. (2013). Liouvillian propagators, riccati equation and differential galois theory. Journal of Physics A: Mathematical and Theoretical, 46(45) doi:10.1088/1751-8113/46/45/455203spa
dc.relation.referencesAcosta-Humanez, P. B. (2010). Galoisian Approach to Supersymmetric Quantum Mechanics.the Integrability Analysis of the Schrodinger Equation by Means of Diérential Galois Theory.spa
dc.relation.referencesAcosta-Humánez, P. B. (2009). Galoisian Approach to Supersymmetric Quantum Mechanics.spa
dc.relation.referencesAcosta-Humánez, P. B. (2009). Nonautonomous hamiltonian systems and morales-ramis theory I. the case ẍ = f(x, t). SIAM Journal on Applied Dynamical Systems, 8(1), 279-297. doi:10.1137/080730329spa
dc.relation.referencesAcosta-Humánez, P. B., Alvarez-Ramírez, M., Blázquez-Sanz, D., & Delgado, J. (2013). Non-integrability criterium for normal variational equations around an integrable subsystem and an example: The wilberforce spring-pendulum. Discrete and Continuous Dynamical Systems- Series A, 33(3), 965-986. doi:10.3934/dcds.2013.33.965spa
dc.relation.referencesAcosta-Humánez, P. B., Álvarez-Ramírez, M., & Delgado, J. (2009). Non-integrability of some few body problems in two degrees of freedom. Qualitative Theory of Dynamical Systems, 8(2), 209-239. doi:10.1007/s12346-010-0008-7spa
dc.relation.referencesAcosta-Humanez, P. B., Blazquez-Sanz, D., & Contreras, C. V. (2009). On hamiltonian potentials with quartic polynomial normal variational equations. Nonlinear Stud.Int.J., 16, 299-314.spa
dc.relation.referencesAcosta-Humánez, P. B., Kryuchkov, S. I., Suazo, E., & Suslov, S. K. (2015). Degenerate parametric amplification of squeezed photons: Explicit solutions, statistics, means and variances. Journal of Nonlinear Optical Physics and Materials, 24(2) doi:10.1142/S0218863515500216spa
dc.relation.referencesAcosta-Humánez, P. B., Lázaro, J. T., Morales-Ruiz, J. J., & Pantazi, C. (2015). On the integrability of polynomial vector fields in the plane by means of picard-vessiot theory. Discrete and Continuous Dynamical Systems- Series A, 35(5), 1767-1800. doi:10.3934/dcds.2015.35.1767spa
dc.relation.referencesAcosta-Humánez, P. B., Morales-Ruiz, J. J., & Weil, J. -. (2011). Galoisian approach to integrability of schrödinger equation. Reports on Mathematical Physics, 67(3), 305-374. doi:10.1016/S0034-4877(11)60019-0spa
dc.relation.referencesAcosta-Humánez, P. B., & Pantazi, C. (2012). Darboux integrals for schrödinger planar vector fields via darboux transformations. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 8 doi:10.3842/SIGMA.2012.043spa
dc.relation.referencesAcosta-Humánez, P. B., & Suazo, E. (2015). Liouvillian propagators and degenerate parametric amplification with time-dependent pump amplitude and phase. Paper presented at the Springer Proceedings in Mathematics and Statistics, , 121 295-307. doi:10.1007/978-3-319-12583-1_21spa
dc.relation.referencesArnold, V. I. (1978). Mathematical methods of classical mechanics. Graduate Texts in Mathematics, 60.spa
dc.relation.referencesAssem, I., Simson, D., & Skowronski, A. (2006). Elements of the Representation Theory of Associative Algebras.spa
dc.relation.referencesAuslander, M., Reiten, I., & Smalø, S. O. (1995). "Representation theory of artin algebras". Representation Theory of Artin Algebras.spa
dc.relation.referencesBleistein, N. (1984). Mathematical Methods for Wave Phenomena.spa
dc.relation.referencesBleistein, N., & Handelsman, R. A. (1986). Asymptotic Expansions of Integrals.spa
dc.relation.referencesČervený, V. (2001). Seismic Ray Theory.spa
dc.relation.referencesDe La Peña, J. (1998). Tame Algebras and Derived Categories.spa
dc.relation.referencesEvans, L. (2010). Partial Differential Equations, Graduate Studies in Mathematics, 19.spa
dc.relation.referencesFritz, J. (1982). Partial differential equations. Applied Mathematical Sciences, 1.spa
dc.relation.referencesGabriel, P. (1972). Manuscripta Mathematica, 6(1), 71-103. doi:10.1007/BF01298413spa
dc.relation.referencesGabriel, P. (1980). Auslander-reiten sequences and representation-finite algebras. Lecture Notes in Mathematics, 831, 1-71.spa
dc.relation.referencesGustafson, W. H. (1982). The history of algebras and their representations. Lecture Notes in Math., 944, 1-28.spa
dc.relation.referencesHerzberger, M. (1958). Modern Geometrical Optics.spa
dc.relation.referencesKaplansky, I. (1957). An Introduction to Differential Algebra.spa
dc.relation.referencesKimura, T. (1969). On riemann's equations which are solvable by quadratures. Funkcial.Ekvac., 12, 269-281.spa
dc.relation.referencesKovacic, J. J. (1986). An algorithm for solving second order linear homogeneous differential equations. Journal of Symbolic Computation, 2(1), 3-43. doi:10.1016/S0747-7171(86)80010-4spa
dc.relation.referencesMagid, A. (1994). Lectures on differential galois theory, university lecture series. American Mathematical Society, Providence, RI.spa
dc.relation.referencesMartinet, J., & Ramis, J. P. (1989). Théorie de galois différentielle et resommation. Computer Algebra and Differential Equations, 117-214.spa
dc.relation.referencesMorales-Ruiz, J. J. (1999). Differential Galois Theory and Non-Integrability of Hamiltonian Systems.spa
dc.relation.referencesMorales-Ruiz, J. J., & Ramis, J. P. (2001). Galoisian obstructions to integrability of hamiltonian systems. Methods Appl.Anal., 8(1), 33-95.spa
dc.relation.referencesMorales-Ruiz, J. J., & Ramis, J. P. (2001). Galoisian obstructions to integrability of hamiltonian systems. Methods Appl.Anal., 8(1), 33-95.spa
dc.relation.referencesMorales-Ruiz, J. J., & Ramis, J. -. (2010). Integrability of dynamical systems through differential galois theory: A practical guide. Differential Algebra, Complex Analysis and Orthogonal Polynomials, 509, 143-220.spa
dc.relation.referencesRauch, J. (2012). Hyperbolic Partial Differential in Geometrical Optics, Graduate Studies in Mathematics, 133.spa
dc.relation.referencesReiten, I. (1985). An introduction to the representation theory of artin algebras. Bulletin of the London Mathematical Society, 17(3), 209-233. doi:10.1112/blms/17.3.209spa
dc.relation.referencesRingel, C. M. (1984). Tame algebras and integral quadratic forms. Tame Algebras and Integral Quadratic Forms.spa
dc.relation.referencesSchleicher, J., Tygel, M., & Hubral, P. (2007). Seismic True-Amplitude Imaging, SEG Geophysical Developments, 12.spa
dc.relation.referencesSinger, M. F. (1990). An outline of differential galois theory. Computer Algebra and Differential Equations , 3-57.spa
dc.relation.referencesVan Der Put, M., & Singer, M. (2003). Galois Theory in Linear Differential Equations, Graduate Text in Mathematics.spa
dc.relation.referencesZworski, M. (2012). Semiclassical Analysis, Graduate Studies in Mathematics, 138spa
dc.type.versioninfo:eu-repo/semantics/publishedVersion
dc.type.driverinfo:eu-repo/semantics/article
dc.identifier.reponamereponame:Repositorio Institucional Universidad de Medellínspa
dc.identifier.instnameinstname:Universidad de Medellínspa


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