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Bäcklund and Darboux transformations. The geometry of solitons. AARMS-CRM workshop, Halifax, Canada, June 4–9, 1999. With short biographies of Albert Victor Bäcklund and Gaston Darboux. (English) Zbl 0974.00040

CRM Proceedings & Lecture Notes. 29. Providence, RI: American Mathematical Society (AMS). xx, 436 p. (2001).

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The articles of this volume will be reviewed individually.
Indexed articles:
Gromak, V. I., Bäcklund transformations of the higher order Painlevé equations, 3-28 [Zbl 1006.34086]
Levi, D.; Ragnisco, O., Dressing method and Bäcklund and Darboux transformations, 29-51 [Zbl 0989.35119]
Rogers, C.; Schief, W. K., The classical geometry of Bäcklund transformations. Introduction to applications in soliton theory, 53-67 [Zbl 0992.35083]
Schief, W. K., An introduction to integrable difference and differential geometries: Affine spheres, their natural generalization and discretization, 69-88 [Zbl 1002.53005]
Aminov, Yu.; Sym, A., On Bianchi and Bäcklund transformations of two dimensional surfaces in four dimensional Euclidean space, 91-93 [Zbl 0999.53004]
Anderson, Ian M.; Fels, Mark E.; Torre, Charles G., Group invariant solutions without transversality and the principle of symmetric criticality, 95-108 [Zbl 0992.58020]
Aratyn, H.; Nissimov, E.; Pacheva, S., Multi-component matrix KP hierarchies as symmetry-enhanced scalar KP hierarchies and their Darboux-Bäcklund solutions, 109-120 [Zbl 0999.37041]
Cieśliński, Jan L., The Darboux-Bäcklund transformation and Clifford algebras, 121-128 [Zbl 0996.37074]
Clarkson, P. A.; Mansfield, E. L.; Webster, H. N., On discrete Painlevé equations as Bäcklund transformations, 129-139 [Zbl 0991.39008]
Clelland, J. N., A Bäcklund transformation for timelike surfaces of constant mean curvature in \(\mathbb{R}^{1,2}\), 141-150 [Zbl 0992.53012]
Corro, A. V.; Ferreira, W.; Tenenblat, K., On Ribaucour transformations, 151-157 [Zbl 1004.53005]
Doliwa, Adam, The Ribaucour congruences of spheres within Lie sphere geometry, 159-166 [Zbl 0994.37039]
Ercolani, N. M., Bäcklund transformations for the reduced Maxwell-Bloch equations, 167-178 [Zbl 1025.37042]
Ferapontov, E. V., Transformations of quasilinear systems originating from the projective theory of congruences, 179-190 [Zbl 1017.53014]
Ferapontov, E. V.; Grundland, A. M., Bäcklund links between different analytic descriptions of constant mean curvature surfaces, 191-197 [Zbl 1001.53014]
Finkel, F., On the integrability of Weingarten surfaces., 199-205 [Zbl 1163.53308]
Finkel, F.; Fokas, A. S., A new immersion formula for surfaces on Lie algebras and integrable equations, 207-216 [Zbl 0989.35118]
Finley, J. D. III, Difficulties with SDiff(2) Toda equation, 217-224 [Zbl 1005.37046]
Havlíček, M.; Pošta, S.; Winternitz, P., Superposition formulas based on nonprimitive group action, 225-231 [Zbl 1004.34006]
Hernandez Heredero, R.; Levi, D.; Rodríguez, M. A.; Winternitz, P., Symmetries of differential difference equations and Lie algebra contractions, 233-243 [Zbl 0994.37033]
Hietarinta, Jarmo, Bäcklund transformations from the bilinear viewpoint, 245-251 [Zbl 0991.35077]
Hlavatý, L., Towards the Lax formulation of SU(2) principal models with nonconstant metric, 253-259 [Zbl 1004.37046]
Hoenselaers, C. A.; Miccichè, S., Transcendental solutions of the sine-Gordon equation, 261-271 [Zbl 0987.35144]
Ioannidou, T.; Piette, B.; Zakrzewski, W. J., Three dimensional Skyrmions and harmonic maps., 273-280 [Zbl 1057.58006]
Konopelchenko, B. G.; Landolfi, G., Induced surfaces and their integrable deformations, 281-289 [Zbl 1002.53001]
Kovalyov, M., Properties of a class of slowly decaying oscillatory solutions of KdV, 291-297 [Zbl 1001.35101]
Lafortune, S.; Ramani, A.; Grammaticos, B.; Ohta, Y.; Tamizhmani, K. M., Blending two discrete integrability criteria: Singularity confinement and algebraic entropy, 299-311 [Zbl 0991.39009]
Ma, Wen-Xiu; Geng, Xianguo, Bäcklund transformations of soliton systems from symmetry constraints, 313-323 [Zbl 1010.37048]
Mathieu, P., Open problems for the super KdV equations, 325-334 [Zbl 0994.37035]
Milson, R., Combinatorial aspects of the Darboux transformation., 335-344 [Zbl 1161.81429]
Musette, M.; Conte, R.; Verhoeven, C., Bäcklund transformation and nonlinear superposition formula of the Kaup-Kupershmidt and Tzitzéica equations, 345-362 [Zbl 0994.35103]
Olver, Peter J.; Sanders, Jan A.; Wang, Jing Ping, Classification of symmetry-integrable evolution equations, 363-372 [Zbl 0995.35005]
Reyes, Enrique G., Integrability of evolution equations and pseudo-spherical surfaces, 373-383 [Zbl 0988.35136]
Rogers, C.; Schief, W. K., Infinitesimal Bäcklund transformations of \(K\)-nets. The 2+1-dimensional sinh-Gordon system, 385-392 [Zbl 0992.35084]
Schief, W. K., Isothermic surfaces and the Calapso equation: The full monty, 393-403 [Zbl 0996.53003]
Schmid, R., Bäcklund transformations induced by symmetries application: Discrete mKdV, 405-410 [Zbl 1010.37049]
Steudel, H., Darboux transformation for a spectral problem quadratic in the spectral parameter, 411-418 [Zbl 0989.35115]
Thomova, Z.; Winternitz, P., Separation of variables and Darboux transformations, 419-427 [Zbl 0991.22015]
Winternitz, P., Bäcklund transformations as nonlinear ordinary differential, or difference equations with superposition formulas, 429-436 [Zbl 0998.34005]

MSC:

00B25 Proceedings of conferences of miscellaneous specific interest
37-06 Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory
35-06 Proceedings, conferences, collections, etc. pertaining to partial differential equations
34-06 Proceedings, conferences, collections, etc. pertaining to ordinary differential equations

Biographic References:

Bäcklund, Albert Victor; Darboux, Gaston
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