Exact solutions of the modified Korteweg-de Vries equation

Theoretical and Mathematical Physics

Volumn 168, Issue 1, 2011, Pages 886-897

  Demontis, F ^a  

^a UNIVERSITY OF CAGLIARI   (Italy)

Author keywords

explicit solution of the modified Korteweg de Vries equation; inverse scattering method; Lyapunov equation

Indexed keywords

EID: 79961146896     PISSN: 00405779     EISSN: 15739333     Source Type: Journal    
DOI: 10.1007/s11232-011-0072-4     Document Type: Article

References (33)

1. S. Matsutani and H. Tsuru, J. Phys. Soc. Japan, 60, 3640-3644 (1991).
2. H. Ono, J. Phys. Soc. Japan, 61, 4336-4343 (1992).
3. E. A. Ralph and L. Pratt, J. Nonlinear Sci., 4, 355-374 (1994).
4. T. S. Komatsu and S.-I. Sasa, Phys. Rev. E, 52, 5574-5582 (1995)
5. arXiv: patt-sol/9506002v1 (1995).
6. T. Nagatani, Phys. A, 265, 297-310 (1999).
7. Z.-P. Li and Y.-C. Liu, Eur. Phys. J. B, 53, 367-374 (2006).
8. H. X. Ge, S. Q. Dai, Y. Xue, and L. Y. Dong, Phys. Rev. E, 71, 066119 (2005).
9. W. K. Schief, Nonlinearity, 8, 1-9 (1995).
10. K. E. Lonngren, Opt. Quant. Electron., 30, 615-630 (1998).
11. A. H. Khater, O. H. El-Kalaawy, and D. K. Callebaut, Phys. Scr., 58, 545-548 (1998).
12. M. Agop and V. Cojocaru, Mater. Trans., 39, 668-671 (1998).
13. V. Ziegler, J. Dinkel, C. Setzer, and K. E. Lonngren, Chaos Solitons Fractals, 12, 1719-1728 (2001).
14. M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations, and Inverse Scattering (London Math. Soc. Lect. Note Ser., Vol. 149), Cambridge Univ. Press, Cambridge (1991).
15. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM Stud. Appl. Math., Vol. 4), SIAM, Philadelphia (1981).
16. M. J. Ablowitz, B. Prinari, and A. D. Trubatch, Discrete and Continuous Nonlinear Schrödinger Systems (London Math. Soc. Lect. Note Ser., Vol. 302), Cambridge Univ. Press, Cambridge (2004).
17. G. L. Lamb Jr., Elements of Soliton Theory, Wiley, New York (1980).
18. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. B. Pitaevskii, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transl.: S. P. Novikov, S. V. Manakov, L. B. Pitaevskii, and V. E. Zakharov, Plenum, New York (1984).
19. V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP, 34, 62-69 (1972).
20. T. Aktosun and C. van der Mee, Inverse Problems, 22, 2165-2174 (2006)
21. arXiv: math-ph/0606008v2 (2006).
22. T. Aktosun, F. Demontis, and C. van der Mee, Inverse Problems, 23, 2171-2195 (2007)
23. arXiv: nlin/0702010v2 (2007).
24. T. Aktosun, F. Demontis, and C. van der Mee, J. Math. Phys., 51, 123521 (2010)
25. arXiv: 1003. 2453v1 [nlin. SI] (2010).
26. F. Demontis and C. van der Mee, Inverse Problems, 24, 025020 (2008).
27. H. Ono, J. Phys. Soc. Japan, 41, 1817-1818 (1976).
28. M. Wadati, J. Phys. Soc. Japan, 34, 1289-1296 (1973).
29. F. Demontis, "Direct and inverse scattering of the matrix Zakharov-Shabat system," Doctoral dissertation, Univ. of Cagliari, Italy (2007).
30. C. van der Mee, "Direct and inverse scattering for skewselfadjoint Hamiltonian systems," in: Current Trends in Operator Theory and its Applications (Oper. Theory Adv. Appl., Vol. 149, J. A. Ball, J. W. Helton, M. Klaus, and L. Rodman, eds.), Birkhäuser, Basel (2004), pp. 407-439.
31. T. N. Busse, "Generalized inverse scattering transform for the nonlinear Schrödinger equation," Doctoral dissertation, Univ. of Texas, Arlington, Texas (2008).
32. H. Bart, I. Gohberg, and M. A. Kaashoek, Minimal Factorization of Matrix and Operator Functions (Oper. Theory Adv. Appl., Vol. 1), Birkhäuser, Basel (1979).
33. H. Dym, Linear Algebra in Action (Grad. Stud. Math., Vol. 78), Amer. Math. Soc., Providence, R. I. (2007).