Higher order terms in multiscale expansions: A linearized kdv hierarchy

Journal of Nonlinear Mathematical Physics

Volumn 9, Issue 3, 2002, Pages 325-346

  Leblond, Hervé ^a  

^a Université d Ang ers   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036055943     PISSN: 14029251     EISSN: 17760852     Source Type: Journal    
DOI: 10.2991/jnmp.2002.9.3.6     Document Type: Article

References (17)

1. Dodd, R K, Eilbeck, J C, Gibbon, J D, and Morris, H C. 1982. Solitons and Nonlinear Wave Equations, London:Academic Press.
2. Flaschka, H, Newell, A C, and Tabor, M. 1991. “Integrability”. In What is Integrability?, Edited by:Zakharov, V E. Berlin:Springer.
3. Gardner, C S, Greene, J M, Kruskal, M D, and Miura, R M. 1967. Method for Solving the Korteweg-de Vries Equation. Phys. Rev. Lett., 19:1095–1097.
4. Hasegawa, A, and Kodama, Y. 1995. Solitons in Optical Telecommunications, New York:Oxford University Press.
5. Joly, J-L, Métivier, G, and Rausch, J. 2000. Transparent Nonlinear Geometric Optics and Maxwell– Bloch Equations. J. Diff. Eqs., 166(1):175–250.
6. Karpman, V I, and Maslov, E M. 1977. Perturbation Theory for Solitons. Sov. Phys. J.E.T.P., 46(2):281–291.
7. Kodama, Y, and Mikhailov, A V. 1997. Obstacles to Asymptotic Integrability, in Algebraic Aspects of Integrable Systems. Progr. Nonlinear Differential Equations Appl., 26:173–204. Birkhaüser Boston, Boston
8. Kodama, Y, and Taniuti, T. 1978. Higher Order Approximation in the Reductive Perturbation Method. I. The Weakly Dispersive System. J. Phys. Soc. Jpn., 45(1):298–310.
9. Korteweg, D J, and Vries, G. 1895. On the Change of Form of Long Waves Advancing in a Rectangular Canal, and on a New Type of Long Stationary Waves. Phil. Mag., 39:422–443.
10. Kraenkel, R A, Manna, M A, Montero, J C, and Pereira, J G. 1995. Boussinesq Solitary Wave as a Multiple-Time Solution of the Korteweg-de Vries Hierarchy. J. Math. Phys., 36(12):6822–6828.
11. Kraenkel, R A, Manna, M A, Montero, J C, and Pereira, J G. 1997. The Role of the Korteweg-de Vries Hierarchy in the N-Soliton Dynamics of the Shallow Water Wave Equation. J. Phys. Soc. Jpn., 66(5):1277–1281.
12. Kraenkel, R A, Manna, M A, and Pereira, J G. 1995. The Korteweg-de Vries Hierarchy and Long Water-Waves. J. Math. Phys., 36(1):307–320.
13. Kraenkel, R A, Manna, M A, and Pereira, J G. 1995. The Reductive Perturbation Method and the Korteweg-de Vries Hierarchy. Acta Appl. Math., 39(1–3):389–403.
14. Lax, P D. 1968. Integrals of Nonlinear Equations of Evolution and Solitary Waves. Commun. Pure Appl. Math., 21:467–490.
15. Leblond, H. 1998. The Secular Solutions of the Linearized KdV Equation. J. Math. Phys., 39(7):3772–3782.
16. Leblond, H. 2001. Solitons in Ferromagnets and the KdV Hierarchy. Nonlinear Phenomena in Complex Systems, 4(1):67–84.
17. Su, C H, and Gardner, C S. 1969. Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation. J. Math. Phys., 10(3):536–539.