Korteweg-de Vries Flow Equations from Manakov Equation by Multiple Scale method

Yıl 2015, Cilt: 3 Sayı: 2, 126 - 132, 19.01.2015

M. Naci Ozer Murat Koparan

Öz

We perform a multiple scales analysis on the modified nonlinear Schr¨odinger (MNLS) equation in the Hamiltonian form.We derive, as amplitude equations, Korteweg-de Vries (KdV) flow equations in the bi-Hamiltonian form

Anahtar Kelimeler

Manakov Equation, Multiple Scale method; Flow Equation

Mehmet Naci Ozer1and Murat Koparan2

Öz

Kaynakça

• S. A. Manakov, On the theory of two-dimensional stationary self-focusing of electromagnetic wawes, Sov. Phys. JETP 38 (1974) 248-2
• B. Crosignani, A. Cutolo, P. di Porto, J. Opt. Soc. Am. 72 (1982) 1136-1141.
• C. R. Menyuk, IEEE JI Quant. Electron. 23 (1987) 174-176.
• J. U. Kang, G. I. Stegeman, J. S. Aitchison, N. Akhmediev, Phys. Rev. Lett. 76 (1996) 3699-3702.
• V. Kutuzov, V. M. Petnikova, V. V. Shuvalov, V. A. Vysloukh, Phys. Rev. E 57 (1998) 6056-6065.
• A. Hasegawa, Y. Kodama, Oxford: Clarendon 1995.
• Y. Kodama, Mathematical theory of NZR. Preprint, solv-int 1997.
• Y. Kodama, A. Maruta, S. Wabnitz, Opt. Lett. 21 (1996) 1815-1817.
• L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, J. Lightwave Tevhnol. 9 (1991) 362-367.
• M. R. Adams, J. Harnad, J. Hurtubise, Commun. Math. Phys. 155 (1993) 385-415.
• E. Alfinito, M. Leo, G. Soliani, L. Solombrino, Phys. Rev. E 53 (1995) 3159-3165.
• C. Polymilis, K. Hizanidis, D. J. Frantzeskakis, Phys. Rev. E 58 (1998) 1112-1124.
• A. V. Porubov, D. F. Parker, Wave Motion. 29 (1999) 97-109.
• V. I. Pulov, I. M. Uzunov, E. J. Chakarov, Phys. Rev. E 57 (1998) 3468-3477.
• P. L. Christiansen, J. C. Eilbeck, V. Z. Enolskii, N. A. Kostov, Proc. R. Soc. Lond. A 456 (2000) 2263-2281.
• R. Radhakrishnan, M. Lakshmanan, J. Hietarinta, Phys. Rev. E 56 (1997) 2213.
• V.E. Zakharov and E.A. Kuznetsov. Multiscale Expansions in The Theory of Systems Integrable by The Inverse Scattering Transform. Physica D, 18 : 455–463, 1986.
• A.P. Fordy. Soliton Theory: A survey of Results, MUP, Manchester, 1990.
• A.P. Fordy and J. Gibbons. Factorisation of operator I. Miura transformations. J. Math. Phys, 21, 2508–2510, 1980.
• A.H. Nayfeh. ”Perturbation Methods” , Wiley , New York , (1973).
• A. R. Osborne and G. Boffetta. A Summable ultiscale Expansion For The KdV Equation. Nonlinear Evolution Equations: Integrability and Spectral Methods., eds. A. Degasperis, A.P.Fordy, M. Lakshmanan, MUP, Manchester and New York, 559–571, 19 M. Koparan, Derivation of Integrable Equations from Nonlinear Partial Equations by Multiple Scales Methods. Ph. D. Eskis¸ehir Osmangazi University, 2008.