Keywords
- Group Element
- Integrability Condition
- Soliton Equation
- Soliton Theory
- Backlund Transformation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A. C. Scott, F. Y. F. Chu and D. W. McLaughlin, Proc. IEEE 61, 1443 (1973).
P. D. Lax, Comm. Pure Appl. Math 21, 467 (1968).
V. E. Zakharov and A. B. Shabat, Soviet Phys. JETP, 34, 62 (1972).
M. J. Ablowitz, D. J. Kaup, A. C. Newell and H. Segur, Stud. Appl. Math., 53, 249 (1974).
V. E. Zakharov and A. V. Mikhailov, Soviet Phys. JETP, 47, 1017 (1978).
D. J. Kaup, A. Rieman, and A. Bers, Rev. Mod. Phys. 51, 275 (1979).
I. M. Gelfand and L. A. Dikii, Funct. Anal. and its Appl., 10, 259 (1976).
H. Chen in Backlund Transformations, Lecture Notes in Mathematics #515, edited by R. Miura (Springer, Berlin 1976).
H. D. Wahlquist and F. B. Estabrook, J. Math. Phys. (N.Y.), 16, 1 (1975).
C. Loewner, Theory of Continuous Groups Notes by H. Flanders and M. H. Protter, (MIT Press, Cambridge, Mass, 1971).
H. Flanders, Differential Forms (Academic Press, New York, 1963).
D. J. Kaup, Lectures on the Estabrook-Wahlquist Method, with Examples of Application, MIT Plasma Research Report, PRR 79/6 (1979).
R. K. Dodd and J. D. Gibbon, Proc. R. Soc. Lond. A. 358, 287 (1977) and 359, 411 (1978).
J. P. Corones in Reference 8.
J. P. Corones, J. Math. Phys. 17, 756 (1976).
For example, N. H. Ibragimov and R. L. Anderson, J. Math. Anal. Applic. 59, 145 (1977), R. J. Oliver, J. Math. Phys. 18, 1212 (1977), S. Kumei, J. Math. Phys, 18, 256 (1977), A. S. Fokas, R. L. Anderson, Lett. Math. Phys., 3, 117 (1979).
C. N. Yang, Phys. Rev. Lett. 33, 445 (1974).
J. P. Corones, B. L. Markovski and V. A. Rizov, J. Math. Phys. 18, 2207 (1977).
L. P. Eisenhart Continuous Groups of Transformations (Princeton U.P., Princeton N. J., 1933).
G. L. Lamb, Phys. Rev. Lett. 37, 235 (1976) and J. Math. Phys. (N.Y.) 18, 1658 (1977).
F. Lund, Phys. Rev. Lett. 38, 1175 (1977) and Phys. Rev. D15, 1540 (1977).
A. Sym and J. Corones, Phys. Rev. Lett. 42, 1099 (1979).
M. Lakshmanan, Phys. Lett. 61A, 53 (1977), and 64A, 353 (1978).
M. Crampin, Phys. Lett. 66A, 243 (1978).
M. Crampin, F. Pirani and D. Robinson, Lett. Math. Phys. 2, 15 (1977).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1980 Springer-Verlag
About this paper
Cite this paper
Corones, J. (1980). Some heuristic comments on solitons, integrability conditions and lie groups. In: Martini, R. (eds) Geometrical Approaches to Differential Equations. Lecture Notes in Mathematics, vol 810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089972
Download citation
DOI: https://doi.org/10.1007/BFb0089972
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10018-8
Online ISBN: 978-3-540-38166-2
eBook Packages: Springer Book Archive
