Bäcklund and Darboux transformations : the geometry of solitons : AARMS-CRM Workshop, June 4-9, 1999, Halifax, N.S., Canada
Bibliographic record
Abstract
Introductory Lectures: Backlund transformations of the higher order Painleve equations by V. I. Gromak Dressing method and Backlund and Darboux transformations by D. Levi and O. Ragnisco The classical geometry of Backlund transformations. Introduction to applications in soliton theory by C. Rogers and W. K. Schief An introduction to integrable difference and differential geometries: Affine spheres, their natural generalization and discretization by W. K. Schief Original Contributions: On Bianchi and Backlund transformations of two dimensional surfaces in four dimensional Euclidean space by Yu. Aminov and A. Sym Group invariant solutions without transversality and the principle of symmetric criticality by I. M. Anderson, M. E. Fels, and C. G. Torre Multi-component matrix KP hierarchies as symmetry-enhanced scalar KP hierarchies and their Darboux-Backlund solutions by H. Aratyn, E. Nissimov, and S. Pacheva The Darboux-Backlund transformation and Clifford algebras by J. L. Cieslinski On discrete Painleve equations as Backlund transformations by P. A. Clarkson, E. L. Mansfield, and H. N. Webster A Backlund transformation for timelike surfaces of constant mean curvature in $\mathbb R^{1,2}$ by J. N. Clelland On Ribaucour transformations by A. V. Corro, W. Ferreira, and K. Tenenblat The Ribaucour congruences of spheres within Lie sphere geometry by A. Doliwa Backlund transformations for the reduced Maxwell-Bloch equations by N. M. Ercolani Transformations of quasilinear systems originating from the projective theory of congruences by E. V. Ferapontov Backlund links between different analytic descriptions of constant mean curvature surfaces by E. V. Ferapontov and A. M. Grundland On the integrability of Weingarten surfaces by F. Finkel A new immersion formula for surfaces on Lie algebras and integrable equations by F. Finkel and A. S. Fokas Difficulties with the SDiff(2) Toda equation by J. D. Finley III Superposition formulas based on nonprimitive group action by M. Havlicek, S. Posta, and P. Winternitz Symmetries of differential difference equations and Lie algebra contractions by R. H. Heredero, D. Levi, M. A. Rodriguez, and P. Winternitz Backlund transformations from the bilinear viewpoint by J. Hietarinta Towards the Lax formulation of SU(2) principal models with nonconstant metric by L. Hlavaty Transcendental solutions of the sine-Gordon equation by C. A. Hoenselaers and S. Micciche Three dimensional skyrmions and harmonic maps by T. Ioannidou, B. Piette, and W. J. Zakrzewski Induced surfaces and their integrable deformations by B. G. Konopelchenko and G. Landolfi Properties of a class of slowly decaying oscillatory solutions of KdV by M. Kovalyov Blending two discrete integrability criteria: Singularity confinement and algebraic entropy by S. Lafortune, A. Ramani, B. Grammaticos, Y. Ohta, and K. M. Tamizhmani Backlund transformations of soliton systems from symmetry constraints by W.-X. Ma and X. Geng Open problems for the super KdV equations by P. Mathieu Combinatorial aspects of the Darboux transformation by R. Milson Backlund transformation and nonlinear superposition formula of the Kaup-Kupershmidt and Tzitzeica equations by M. Musette, R. Conte, and C. Verhoeven Classification of symmetry-integrable evolution equations by P. J. Olver, J. A. Sanders, and J. P. Wang Integrability of evolution equations and pseudo-spherical surfaces by E. G. Reyes Infinitesimal Backlund transformations of $K$-nets. The 2 + 1 - dimensional Sinh-Gordon system by C. Rogers and W. K. Schief Isothermic surfaces and the Calapso equation: The full Monty by W. K. Schief Backlund transformations induced by symmetries. Application: Discrete mKdV by R. Schmid Darboux transformation for a spectral problem quadratic in the spectral parameter by H. Steudel Separation of variables and Darboux transformations by Z. Thomova and P. Winternitz Backlund transformations as nonlinear ordinary differential, or difference equations with superposition formulas by P. Winternitz.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.004 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.054 | 0.013 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".