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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).
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Research supported in part by Polish Ministry of Science, Higher Education and Technology. Grant M.R.I.7.
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Sym, A. Soliton surfaces. Lett. Nuovo Cimento 33, 394–400 (1982). https://doi.org/10.1007/BF02725614
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DOI: https://doi.org/10.1007/BF02725614