Year 2015,
Volume: 3 Issue: 2, 126 - 132, 19.01.2015
Abstract
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
References
- 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.
Year 2015,
Volume: 3 Issue: 2, 126 - 132, 19.01.2015
Abstract
References
- 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.
There are 21 citations in total.
Details
| Journal Section | Articles |
|---|---|
| Authors | |
| Publication Date | January 19, 2015 |
| Published in Issue | Year 2015 Volume: 3 Issue: 2 |