This is a preview of subscription content, log in via an institution to check access.
References
G. L. Lamb: inBäcklund Transformations, edited byR. M. Miura (Berlin, Heidelberg, New York, N. Y., 1976).
L. P. Eisenhart:A Treatise on the Differential Geometry of Curves and Surfaces (New York, N. Y., 1960);L. P. Eisenhart:An Introduction to Differential Geometry (Princeton, N. J., 1940).
R. Sasaki:Phys. Lett. A,71, 390 (1979);R. Sasaki:Nucl. Phys. B,154, 343 (1979).
B. M. Barbashov andV. V. Nesterenko:Fortschr. Phys.,28, 427 (1980).
K. Pohlmeyer:Commun. Math. Phys.,46, 207 (1976);F. Lund andT. Regge:Phys. Rev. D,14, 1524 (1976);B. Getmanov:Ž. Ėksp. Teor. Fiz. Pis’ma Red.,25, 132 (1977).
F. Lund:Ann. Phys. (N. Y.),115, 251 (1978).
M. S. Marinov:Yad. Fiz.,28, 251 (1978);A. Sym andJ. Corones:Phys. Rev. Lett.,42, 1099 (1979);G. Reiter:J. Math. Phys. (N. Y.),21, 2704 (1980). The Lund-Regge approach is gaugeequivalent to the Lamb approach presented inG. L. Lamb:J. Math. Phys. (N. Y.),18, 1654 (1977).
M. Gürses andY. Nutku:J. Math. Phys. (N. Y.),22, 1393 (1981).
D. J. Struik:Lectures on Classical Differential Geometry (London, 1961).
L. P. Eisenhart:Riemannian Geometry (Princeton, N. J., 1949).
A. Sym:Soliton theory is surface theory, preprint IFT/11/81.
M. J. Ablowitz, D. J. Kaup, A. C. Newell andH. Segur:Stud. Appl. Math.,53, 249 (1974).
R. L. Anderson andN. H. Ibragimov:Lie-Bäcklund Transformation in Applications (Siam, Philadelphia, Pa., 1979).
L. Bianchi:Lezioni di geometria differenziale (Pisa, 1922).
A. O. Barut andR. Raczka:Theory of Group Representations and Applications (Warsaw, 1977);B. G. Wybourne:Classical Groups for Physicists (New York, N. Y., London, Sydney, and Toronto, 1974).
S. J. Orfanidis:Phys. Rev. D,21, 1513 (1980).
V. E. Zakharov, S. V. Manakov, S. P. Novikov andL. P. Pitaevski:Theory of Solitons (Moscow, 1980) (in Russian);S. Manakov:Sov. Sci. Rev. Phys. Rev.,1, 133 (1979).
A. Sym andJ. Corones:Phys. Lett. A,68, 305 (1978).
This important observation is due toJ. Tafel.
The equation Φ, ζ=Φr is, modulo the order of Φ andr matrices, the second equation of the deformation theory, see for exampleH. Flaschka andA. C. Newell:Commun. Math. Phys.,76, 65 (1980). This remark is due toD. Levi.
M. Crampin:Phys. Lett. A,66, 170 (1978).
W. A. Blaschke:Einführung in die Differentialgeometrie (Berlin, 1930).
F. J. Chinea:Phys. Rev. D,24, 1053 (1981).
V. A. Belinsky andV. E. Zakharov:Ž. Ėksp. Teor. Fiz.,75, 1953 (1978);D. Maison:Phys. Rev. Lett.,42, 521 (1978);G. Neugebauer:Phys. Lett. A,75, 259 (1980).
W. Kinnersley: inGeneral Relativity and Gravitation, edited byG. Shaviv andJ. Rosen (New York, N. Y., 1975).
K. Konno andM. Wadati:Prog. Theor. Phys.,52, 1652 (1975).
D. Levi andO. Ragnisco:Bäcklund transformations for chiral field equations, preprint No. 268 1981. Istituto di Fisica, Universitàa di Roma, Italy,Phys. Lett. A (in press).
Author information
Authors and Affiliations
Additional information
Research supported in part by Polish Ministry of Science, Higher Education and Technology. Grant M.R.I.7.
Rights and permissions
About this article
Cite this article
Sym, A. Soliton surfaces. Lett. Nuovo Cimento 33, 394–400 (1982). https://doi.org/10.1007/BF02725614
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02725614