Periodic solutions of a derivative nonlinear Schrödinger equation: Elliptic integrals of the third kind

Journal of Computational and Applied Mathematics

Volumn 235, Issue 13, 2011, Pages 3825-3830

  Chow, K W ^a   Ng, T W ^a  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Derivative nonlinear Schr dinger (ChenLeeLiu) equation; Elliptic integrals of the third kind

Indexed keywords

ABSOLUTE VALUES; COMPLEX ENVELOPE; COUNTABLE SET; DINGER EQUATION; ELLIPTIC FUNCTIONS; ELLIPTIC INTEGRALS; ENVELOPE EQUATIONS; FEATURE CONTRASTS; NONLINEAR EFFECT; PERIODIC SOLUTION; PLASMA PHYSICS; WAVE-PACKET DYNAMICS;

GEOMETRY; PROBLEM SOLVING;

NONLINEAR EQUATIONS;

EID: 79955570574     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2011.01.029     Document Type: Conference Paper

References (35)

1. C.C. Mei The Applied Dynamics of Ocean Surface Waves 1989 World Scientific Singapore
2. N.N. Akhmediev, and A. Ankiewicz Solitons: Nonlinear Pulses and Beams 1997 Chapman and Hall London
3. S. Trillo, and W. Torruellas Spatial Solitons 2001 Springer Berlin
4. Y.S. Kivshar, and G.P. Agrawal Optical Solitons: From Fibers to Photonic Crystals 2003 Academic Press San Diego
5. M.J. Ablowitz, and H. Segur Solitons and the Inverse Scattering Transform 1981 SIAM Philadelphia
6. B.A. Malomed Soliton Management in Periodic Systems 2006 Springer New York
7. H.H. Chen, Y.C. Lee, and C.S. Liu Integrability of nonlinear Hamiltonian systems by inverse scattering method Physica Scripta 20 1979 490 492
8. A. Nakamura, and H.H. Chen Multi-soliton solutions of a derivative nonlinear Schrödinger equation Journal of the Physical Society of Japan 49 1980 813 816
9. D. Pelinovsky, J. Springael, F. Lambert, and I. Loris On modified NLS, Kaup, and NLBq equations: differential transformations and bilinearization Journal of Physics A 30 1997 8705 8717 (Pubitemid 127613553)
10. A.G. Meshkov Integrability and integrodifferential substitutions Journal of Mathematical Physics 38 1997 6428 6443
11. T. Tsuchida, and M. Wadati New integrable systems of derivative nonlinear Schrödinger equations with multiple components Physics Letters A 257 1999 53 64
12. Y.C. Hon, and E.G. Fan Uniformly constructing finite-band solutions for a family of derivative nonlinear Schrödinger equations Chaos, Solitons & Fractals 24 2005 1087 1096 (Pubitemid 40146213)
13. J. Moses, B.A. Malomed, and F.W. Wise Self-steepening of ultrashort optical pulses without self-phase-modulation Physical Review A 76 2007 021802
14. Y.C. Ma Perturbed plane wave solutions of the cubic Schrödinger equation Studies in Applied Mathematics 60 1979 43 58
15. D.H. Peregrine Water waves, nonlinear Schrödinger equations and their solutions Journal of the Australian Mathematical Society, Series BApplied Mathematics 25 1983 16 43
16. D. Mihalache, F. Lederer, and D.M. Baboiu Two-parameter family of exact solutions of the nonlinear Schrödinger equation describing optical soliton propagation Physical Review A 47 1993 3285 3290 (Pubitemid 23667252)
17. K.W. Chow Solitary waves on a continuous wave background Journal of the Physical Society of Japan 64 1995 1524 1528
18. N.A. Kostov, and I.M. Uzunov New kinds of periodic waves in birefringent optical fibers Optics Communications 89 1992 389 392
19. M. Florjanczyk, and R. Tremblay Symbiotic periodic waves in a nonlinear birefringent fiber Optics Communications 105 1994 405 409
20. F.T. Hioe Solitary waves and N coupled nonlinear equations Journal of Physics A 32 1999 1217 1233
21. N. Akhmediev, and A. Ankiewicz First order exact solutions of the nonlinear Schrödinger equation in the normal dispersion regime Physical Review A 47 1993 3213 3221 (Pubitemid 23667260)
22. K.W. Chow A class of doubly periodic waves for nonlinear evolution equations Wave Motion 35 2002 71 90 (Pubitemid 33122625)
23. P.L. Christiansen, J.C. Eilbeck, V.Z. Enolskii, and N.A. Kostov Quasi-periodic and periodic solutions for coupled nonlinear Schrödinger equations of the Manakov type Proceedings of the Royal Society of London A 456 2000 2263 2281
24. J.C. Bronski, L.D. Carr, B. Deconinck, J.N. Kutz, and K. Promislow Stability of repulsive BoseEinstein condensates in a periodic potential Physical Review E 63 2001 036612 (11 pages)
25. N.A. Kostov, V.Z. Enolskii, V.S. Gerdjikov, V.V. Konotop, and M. Salerno Two-component Bose Einstein condensates in periodic potential Physical Review E 70 2004 056617 (12 pages)
26. H.J. Shin Squared wave functions approach to periodic solutions of vector nonlinear Schrödinger equation Journal of Physics A 36 2003 4113 4126
27. T. Woodcock, O.H. Warren, and J.N. Elgin Genus two finite gap solutions to the vector nonlinear Schrödinger equation Journal of Physics A 40 2007 F355 F361
28. M.A. Abdou An improved generalized F-expansion method and its applications Journal of Computational and Applied Mathematics 214 2008 202 208 (Pubitemid 351227370)
29. Y. Matsuno Bilinear Transformation Method 1984 Academic Press Orlando
30. A.M. Kamchatnov Nonlinear Periodic Waves and Their Modulations 2000 World Scientific Singapore
31. B.C. Carlson Jacobian elliptic functions as inverses of an integral Journal of Computational and Applied Mathematics 174 2005 355 359 (Pubitemid 40046854)
32. D. Karp, A. Savenkova, and S.M. Sitnik Series expansions for the third complete elliptic integrals via partial fraction decomposition Journal of Computational and Applied Mathematics 207 2007 331 337 (Pubitemid 47102008)
33. L. Urankar, P. Henninger, and F.S. Nestel Compact extended algorithms for elliptic integrals in electromagnetic field and potential computations Part II: elliptic integral of third kind with extended integration range IEEE Transactions on Magnetics 30 1994 1236 1241
34. H. Ezure Attenuation function of radiation from disk source with direction in cosine distribution Journal of Nuclear Science and Technology 45 2008 773 783
35. D.F. Lawden Elliptic Functions and Applications 1989 Springer New York