Orbital stability for stationary solutions of the Wadati-Konno-Ichikawa- Shimizu equation

Journal of the Physical Society of Japan

Volumn 82, Issue 6, 2013, Pages

  VAN Gorder, Robert A ^a  

^a UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

Orbital stability; Stationary solution; Wadati Konno Ichikawa Shimizu (WKIS) equation

Indexed keywords

EID: 84878952222     PISSN: 00319015     EISSN: 13474073     Source Type: Journal    
DOI: 10.7566/JPSJ.82.064005     Document Type: Article

References (25)

1. V. Gerdjikov, G. Vilasi, and A. B. Yanovski: Integrable Hamiltonian Hierarchies: Spectral and Geometric Methods (Springer, Heidelberg, 2008) Lecture Notes in Physics, Vol. 748.
2. F. Calogero and A. Degasperis: Spectral Transform and Solitons: Tools to Solve and Investigate Nonlinear Evolution Equations (Elsevier, Amsterdam, 1982) Studies in Mathematics and Its Applications, Vol. 13.
3. M. Wadati, K. Konno, and Y.-H. Ichikawa: J. Phys. Soc. Jpn. 46 (1979) 1965.
4. T. Shimizu and M. Wadati: Prog. Theor. Phys. 63 (1980) 808.
5. M. Lakshmanan and S. Ganesan: J. Phys. Soc. Jpn. 52 (1983) 4031.
6. M. Lakshmanan and S. Ganesan: Physica A 132 (1985) 117.
7. M. Boiti, V. S. Gerdjikov, and F. Pempinelli: Prog. Theor. Phys. 75 (1986) 1111.
8. X. Ying, Z. Ruguang, and W. Jianwen: J. Xuzhou Norm. Univ. (Natural Science Edition) 4 (2011) 27.
9. R. A. Van Gorder: Prog. Theor. Phys. 128 (2012) 993.
10. H. Hasimoto: J. Phys. Soc. Jpn. 31 (1971) 293.
11. R. A. Van Gorder: Theor. Comput. Fluid Dyn. 26 (2012) 591.
12. R. A. Van Gorder: Phys. Rev. E 86 (2012) 057301.
13. R. A. Van Gorder: J. Fluid Mech. 707 (2012) 585.
14. M. G. Vakhitov and A. A. Kolokolov: Sov. Radiophys. 16 (1973) 783.
15. V. G. Makhankov, Y. P. Rybakov, and V. I. Sanyuk: Phys.-Usp. 37 (1994) 113.
16. D. V. Skryabin and W. J. Firth: Phys. Rev. E 58 (1998) R1252.
17. P. Lundquist, D. R. Andersen, and Yu. S. Kivshar: Phys. Rev. E 57 (1998) 3551.
18. D. Mihalache, D. Mazilu, and L. Torner: Phys. Rev. Lett. 81 (1998) 4353.
19. E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth: Phys. Rev. Lett. 83 (1999) 296.
20. Y. V. Kartashov, V. A. Vysloukh, and L. Torner: Phys. Rev. Lett. 93 (2004) 093904.
21. F. G. Mertens, N. R. Quintero, and A. R. Bishop: Phys. Rev. E 81 (2010) 016608.
22. M. Blaauboer, B. A. Malomed, and G. Kurizki: Phys. Rev. Lett. 84 (2000) 1906.
23. N. N. Rosanov, A. G. Vladimirov, D. V. Skryabin, and W. J. Firth: Phys. Lett. A 293 (2002) 45.
24. B. A. Malomed, D. J. Kaup, and R. A. Van Gorder: Phys. Rev. E 85 (2012) 026604.
25. J. Yang: Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, Philadelphia, PA, 2010).