Approach to first-order exact solutions of the Ablowitz-Ladik equation

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 83, Issue 5, 2011, Pages

  Ankiewicz, Adrian ^a   Akhmediev, Nail ^a   Lederer, Falk ^b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX FUNCTIONS; DINGER EQUATION; EXACT SOLUTION; FIRST-ORDER; IMAGINARY PARTS; INDEPENDENT PARAMETERS; NOVEL TECHNIQUES;

NONLINEAR EQUATIONS;

EID: 79961073398     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.83.056602     Document Type: Article

References (27)

1. A. Montina, U. Bortolozzo, S. Residori, and F. T. Arecchi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.173901 103, 173901 (2009).
2. A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.53.1172 53, 1172 (1996).
3. P. Marquie, J. M. Bilbault, and M. Remoissenet, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.51.6127 51, 6127 (1995).
4. J. M. Bilbault and P. Marquie, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.53.5403 53, 5403 (1996).
5. D. Hennig and G. P. Tsironis, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(98)00025-8 307, 333 (1999).
6. P. D. Miller, Commun. Pure Appl. Math. PRPLCM 0010-3640 10.1002/cpa.3160481203 48, 1369 (1995).
7. N. N. Akhmediev and V. I. Korneev, Teor. Mat. Fiz. TMPHAH 0040-5779 10.1007/BF01037866 69, 189 (1986);
8. N. N. Akhmediev and V. I. Korneev, [Theor. Math. Phys.(USSR) 0040-5779 10.1007/BF01037866 69, 1089 (1986)].
9. N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, Teor. Mat. Fiz. TMPHAH 0040-5779 10.1007/BF01017105 72, 809 (1986).
10. N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, [Theor. Math. Phys. (USSR) 72, 183 (1987)].
11. N. Akhmediev and A. Ankiewicz, Solitons (Chapman and Hall, London, 1997).
12. M. J. Ablowitz and J. F. Ladik, Stud. Appl. Math. 55, 213 (1976).
13. M. J. Ablowitz and J. F. Ladik, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.523009 17, 1011 (1976).
14. N. Akhmediev and A. Ankiewicz, Phys. Rev. E 1539-3755 10.1103/PhysRevE.83.046603 83, 046603 (2011).
15. A. Ankiewicz, N. Akhmediev, and J. M. Soto-Crespo, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.026602 82, 026602 (2010).
16. K. Narita, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.59.3528 59, 3528 (1990).
17. D. H. Peregrine, J. Aust. Math. Soc. Series B JAMMDU 0334-2700 10.1017/S0334270000003891 25, 16 (1983).
18. V. I. Shrira and V. V. Geogjaev, J. Eng. Math. JLEMAU 0022-0833 10.1007/s10665-009-9347-2 67, 11 (2010).
19. N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2008.12.036 373, 675 (2009).
20. K. B. Dysthe and K. Trulsen, Phys. Scr. PHSTBO 0031-8949 10.1238/Physica.Topical.082a00048 T82, 48 (1999).
21. V. V. Voronovich, V. I. Shrira, and G. Thomas, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112008001171 604, 263 (2008). (Pubitemid 351709340)
22. I. Ten and H. Tomita, "Simulation of the ocean waves and appearance of freak waves," Reports of RIAM Symposium No. 17SP1-2
23. Proceedings of a symposium held at Chikushi Campus, Kyushu University, Kasuga, Fukuoka, Japan, March 10-11, 2006.
24. D. Clamond, M. Francius, J. Grue, and C. Kharif, European J. Mech. B - Fluids EJBFEV 0997-7546 10.1016/j.euromechflu.2006.02.007 25, 536 (2006). (Pubitemid 44226510)
25. N. Akhmediev, and, E. Pelinovsky, (editors), "Rogue waves-toward a unifying concept," Special Issue of Eur. Phys. J. Special Topics 185 (2010).
26. B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nature Phys. EJBFEV 1745-2473 10.1038/nphys1740 6, 790 (2010).
27. K. Chow, R. Conte, and N. Xu, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2005.09.053 349, 422 (2006). (Pubitemid 43021038)