Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-07T10:26:44.988Z Has data issue: false hasContentIssue false
  • English
  • Français

Interaction of some meromorphic solutions of the KdV equation

Published online by Cambridge University Press:  20 January 2009

M. Kovalyov  and
K. M. Lee
M. Kovalyov
Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, CanadaT6G 2G1
K. M. Lee
Affiliation:
Department of Mathematics, Science and Technology, Heartland Community College, 1226 Tow Anda Avenue, Bloomington Illinois 61701, USA
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A necessary and sufficient condition for confluence of two poles of a class of meromorphic solutions of the KdV equation is introduced and proved.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 2 , June 1999 , pp. 341 - 348
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

1.Ablowitz, M. J. and Clarkson, P. A., Solitons, Nonlinear Evolution Equations and Inverse Scattering (London Math. Society Lecture Notes), 149, Cambridge University Press, 1991).CrossRefGoogle Scholar
2.Caenepeel, S. and Malfliet, W., Internal structure of the two-soliton solutions of the KdV equation, Wave Motion 7 (1985), 299–305.CrossRefGoogle Scholar
3.Fuchssteiner, B., The interaction equation, Phys. A 228 (1996), 189–211.CrossRefGoogle Scholar
4.Gardner, C. S., Greene, J. M., Kruskal, M. D. and Miura, R. M., Korteweg-de Vries equation and generalizations VI, Comm. Pure Appl. Math. 27 (1974), 97–133.CrossRefGoogle Scholar
5.Hodnett, P. F. and Moloney, T. P., On the structure during interaction of the two-soliton solution of the Korteweg-de Vries equation, SIAM J. Appl. Math. 49 (1989), 1174–1187.CrossRefGoogle Scholar
6.Hu, H., Darboux transformation of Su-chain, in Proc. Conf. Diff. Geometry in honor of Prof. Su Buchin (1991, Shanghai, World Scientific Press, Singapore, 1993).Google Scholar
7.Kovalyov, M., Basic motions of the Korteweg-de Vries equation, in Nonlinear Analysis, Theory. Methods and Applications, to appear.Google Scholar
8.Levitan, B. M., Inverse Sturm-Liouville Problems (Chapter 6, VNU Science Press, 1987).CrossRefGoogle Scholar
9.LeVeque, R. J., On the interaction of nearly equal solitons in the KdV equation, SIAM J. Appl. Math. 47 (1987), 254–262.CrossRefGoogle Scholar
10.Malfliet, W. and Van de Velde, L., A study of two interacting KdV solitons, Lett. Nuovo Cimento (2) 42 (1985), 179–183.CrossRefGoogle Scholar
11.Matveev, V. B., Asymptotics of the multiPosition-Soliton τ-function of the Kortewegde Vries equation and the supertransparency, J. Math. Phys. 35 (1994), 2955.CrossRefGoogle Scholar
12.Matveev, V. B., Phys. Lett. A. 135 (1992), 2009–2212.Google Scholar
13.Moloney, T. P. and Hodnett, P. F., Soliton interaction (for the Korteweg-de Vries equation): a new perspective, J. Phys. A 19 (1986), L1129–L1135.CrossRefGoogle Scholar
14.Stahlhofen, A. A., On completely transparent potentials of the Shrödinger equation, Phys. Rev. A51 (1995), 934.CrossRefGoogle Scholar
15.Stahlhofen, A., Ann. der Physik 1 (1992), 554–569.CrossRefGoogle Scholar
16.Yoneyama, T., The Korteweg-de Vries two-soliton solution as interacting two single solitons, Progr. Theoret. Phys. 71 (1984), 843–846.CrossRefGoogle Scholar