najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2015-6-2-198-204najo-911Research ArticlePAPERS, PRESENTED AT THE CONFERENCEPAPERS, PRESENTED AT THE CONFERENCECauchy problem for the linearized KdV equation on general metric star graphsSobirovZ. A.

Faculty of Mathematics; Applied Mathematics Department

Vuzgorodok, 100047 Tashkent

100000 Tashkent

AkhmedovM. I.

Applied Mathematics Department

100000 Tashkent

UeckerH.

Institut f¨ur Mathematik

D26111 Oldenburg

hannes.uecker@uni-oldenburg.deNational University of Uzbekistan; Tashkent Financial InstituteUzbekistanTashkent Financial InstituteUzbekistanUniversit¨at OldenburgGermany20151408202562198204Copyright © Sobirov Z.A., Akhmedov M.I., Uecker H., 20252025Sobirov Z.A., Akhmedov M.I., Uecker H.Sobirov Z.A., Akhmedov M.I., Uecker H.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/911

.

KdVinitial value problemPDE on metric graphsexact solutionthird order differential equationWe gratefully thank the Volkswagen Stiftung for financial support.ReferencesS. Abdinazarov. The general boundary value problem for the third order equation with multiple characteristics (in Russian). Differential Equations, 13 (1), P. 3–12 (1981).S. Abdinazarov. The general boundary value problem for the third order equation with multiple characteristics (in Russian). Differential Equations, 13 (1), P. 3–12 (1981).J.L. Bona and A.S. Fokas. Initial-boundary-value problems for linear and integrable nonlinear dispersive partial differential equations. Nonlinearity, 21, P. 195–203 (2008).J.L. Bona and A.S. Fokas. Initial-boundary-value problems for linear and integrable nonlinear dispersive partial differential equations. Nonlinearity, 21, P. 195–203 (2008).L. Cattabriga. Unproblema al contorno per unaequazione parabolica di ordine dispari. Annali della Scuola Normale Superiore di Pisa, 13 (3), P.163–203 (1959).L. Cattabriga. Unproblema al contorno per unaequazione parabolica di ordine dispari. Annali della Scuola Normale Superiore di Pisa, 13 (3), P.163–203 (1959).J.E. Colliander and C.E. Kenig. The generalized Korteweg-de Vries equation on the half line. Commun. Partial Differ. Equations, 27 (11–12), P. 2187–2266 (2002).J.E. Colliander and C.E. Kenig. The generalized Korteweg-de Vries equation on the half line. Commun. Partial Differ. Equations, 27 (11–12), P. 2187–2266 (2002).T.D. Djuraev. Boundary value problems for mixed and mixid-composite type equations, (in russian). Fan, Tashkent, 1979.T.D. Djuraev. Boundary value problems for mixed and mixid-composite type equations, (in russian). Fan, Tashkent, 1979.A.V. Faminskii and N.A. Larkin. Initial-boundary value problems for quasilinear dispersive equations posed on a bounded interval. Electron. J. Differ. Equ., 1, P. 1–20 (2010).A.V. Faminskii and N.A. Larkin. Initial-boundary value problems for quasilinear dispersive equations posed on a bounded interval. Electron. J. Differ. Equ., 1, P. 1–20 (2010).A.S. Fokas and L.Y. Sung. Initial boundary value problems for linear dispersive evolution equations on the half line. Industrial Mathematics Institute Preprint Series, 11, P. 1–29 (1999).A.S. Fokas and L.Y. Sung. Initial boundary value problems for linear dispersive evolution equations on the half line. Industrial Mathematics Institute Preprint Series, 11, P. 1–29 (1999).M. Rahimy. Applications of fractional differential equations. Applied Mathematical Sciences, 4 (50), P. 2453–2461 (2010).M. Rahimy. Applications of fractional differential equations. Applied Mathematical Sciences, 4 (50), P. 2453–2461 (2010).R. Gorenflo and F. Mainard. Fractional calculus: Integral and differential equations of fractional order. ArXiv:0805.3823v1 (2008).R. Gorenflo and F. Mainard. Fractional calculus: Integral and differential equations of fractional order. ArXiv:0805.3823v1 (2008).E. Taflin. Analytic linearization of the Korteweg-De Vries equation. Pacific Journal Of Mathematics, 108 (1), P. 203–220 (1983).E. Taflin. Analytic linearization of the Korteweg-De Vries equation. Pacific Journal Of Mathematics, 108 (1), P. 203–220 (1983).V. Belashov and S. Vladimirov. Solitary waves in dispersive complex media: theory, simulation, application. Springer, 2005.V. Belashov and S. Vladimirov. Solitary waves in dispersive complex media: theory, simulation, application. Springer, 2005.G.B. Whitham. Linear and nonlinear waves. Pure and Applied Mathematics, Wiley-Interscience, 1974.G.B. Whitham. Linear and nonlinear waves. Pure and Applied Mathematics, Wiley-Interscience, 1974.Z.A. Sobirov, H. Uecker and M. Akhmedov. Exact solutions of the Cauchy problem for the linearized KdV equation on metric star graphs. Uz. Math. J., to appear. Preprint: http://www.staff.uni-oldenburg.de/hannes.uecker/pre/049-lkdvgr.pdf.Z.A. Sobirov, H. Uecker and M. Akhmedov. Exact solutions of the Cauchy problem for the linearized KdV equation on metric star graphs. Uz. Math. J., to appear. Preprint: http://www.staff.uni-oldenburg.de/hannes.uecker/pre/049-lkdvgr.pdf.

The authors declare that there are no conflicts of interest present.