Cauchy problem for the linearized KdV equation on general metric star graphs

KdV, initial value problem, PDE on metric graphs, exact solution, third order differential equation

1. 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).

2. 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).

3. L. Cattabriga. Unproblema al contorno per unaequazione parabolica di ordine dispari. Annali della Scuola Normale Superiore di Pisa, 13 (3), P.163–203 (1959).

4. 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).

5. T.D. Djuraev. Boundary value problems for mixed and mixid-composite type equations, (in russian). Fan, Tashkent, 1979.

6. 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).

7. 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).

8. M. Rahimy. Applications of fractional differential equations. Applied Mathematical Sciences, 4 (50), P. 2453–2461 (2010).

9. R. Gorenflo and F. Mainard. Fractional calculus: Integral and differential equations of fractional order. ArXiv:0805.3823v1 (2008).

10. E. Taflin. Analytic linearization of the Korteweg-De Vries equation. Pacific Journal Of Mathematics, 108 (1), P. 203–220 (1983).

11. V. Belashov and S. Vladimirov. Solitary waves in dispersive complex media: theory, simulation, application. Springer, 2005.

12. G.B. Whitham. Linear and nonlinear waves. Pure and Applied Mathematics, Wiley-Interscience, 1974.

13. 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.