Traveling wave solutions of a generalized modified Kadomtsev-Petviashvili equation

Journal of Mathematical Physics

Volumn 45, Issue 6, 2004, Pages 2181-2187

  Schurmann H W ^a   Serov, V S ^b  

^a UNIVERSITY OF OSNABRÜCK   (Germany)

^b UNIVERSITY OF OULU   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2942650959     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1737813     Document Type: Article

References (19)

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2. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM, Philadelphia, 1981); M. J. Ablowitz and P. Clarkson, Solitons, Nonlinear Evolution Equations, and Inverse Scattering (Cambridge University Press, Cambridge, 1991).
3. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM, Philadelphia, 1981); M. J. Ablowitz and P. Clarkson, Solitons, Nonlinear Evolution Equations, and Inverse Scattering (Cambridge University Press, Cambridge, 1991).
4. S. Turitsyn and G. Falkovich, Sov. Phys. JETP 62, 1 (1985).
5. X. P. Wang, M. J. Ablowitz, and H. Segur, Physica D 78, 241 (1994).
6. J. C. Saut, Acta Appl. Math. 39, 477 (1995).
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8. H. H. Dai and X. Geng, J. Math. Phys. 41, 7501 (2000).
9. J. C. Saut, Indiana Univ. Math. J. 42, 1011 (1993).
10. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, 1927), pp. 452-455.
11. H. W. Schumann, Phys. Rev. E 54, 4312 (1996).
12. In Ref. 9, p. 454 and Ref. 10, Eq. (11).
13. In Ref. 9, p. 453.
14. K. Chandrasekharan, Elliptic Functions (Springer, Berlin, 1985), p. 44.
15. Handbook of Mathematical Functions, edited by M. Abramowitz and J. Stegun (Dover, New York, 1968), p. 629.
16. In Ref. 10, Eq. (14) with sript p sign substituted according to (18.12.3) in Ref. 14.
17. See, P. G. Drazin and R. S. Johnson, Solitons; An Introduction (Cambridge University Press, Cambridge 1988), p. 23 and Ref. 10, Fig. 1.
18. In Ref. 14, Eq. (18.12.3), p. 651.
19. For q<0 we disregard unbounded solutions f(z) that satisfy R(f)≥0, f ≠ 0 (cf. Fig. 1, 3 ≤f<∞ in (b), - ∞