Abstract:
In the classification of partial differential equations, one cannot avoid the use of invertible changes of variables, which include not only the long-known point and contact transformations but also, for example, so-called symmetric and generalized contact transformations (reviewed by Mikhailov, Shabat, and Yamilov [1]). The present paper considers a further class of invertible changes of variables.
Citation:
R. I. Yamilov, “Invertible changes of variables generated by Bäcklund transformations”, TMF, 85:3 (1990), 368–375; Theoret. and Math. Phys., 85:2 (1990), 1269–1275
This publication is cited in the following 27 articles:
S Ya Startsev, “Darboux integrability of hyperbolic partial differential equations: is it a property of integrals rather than equations?”, J. Phys. A: Math. Theor., 58:2 (2025), 025206
R. N. Garifullin, “Classification of semidiscrete equations of hyperbolic type. The case of fifth-order symmetries”, Theoret. and Math. Phys., 222:1 (2025), 10–19
V. E. Adler, “3D consistency of negative flows”, Theoret. and Math. Phys., 221:2 (2024), 1836–1851
R. N. Garifullin, “Classification of semidiscrete equations of hyperbolic type. The case of third-order symmetries”, Theoret. and Math. Phys., 217:2 (2023), 1767–1776
S. Ya. Startsev, “On Bäcklund Transformations Preserving the Darboux Integrability of Hyperbolic Equations”, Lobachevskii J Math, 44:5 (2023), 1929
Ufa Math. J., 13:2 (2021), 107–114
R. N. Garifullin, “On integrability of semi-discrete Tzitzeica equation”, Ufa Math. J., 13:2 (2021), 15–21
Ufa Math. J., 13:2 (2021), 160–169
Garifullin R.N. Habibullin I.T., “Generalized Symmetries and Integrability Conditions For Hyperbolic Type Semi-Discrete Equations”, J. Phys. A-Math. Theor., 54:20 (2021), 205201
R. N. Garifullin, R. I. Yamilov, “Modified series of integrable discrete equations on a quadratic lattice with a nonstandard symmetry structure”, Theoret. and Math. Phys., 205:1 (2020), 1264–1278
Garifullin R.N. Gubbiotti G. Yamilov I R., “Integrable Discrete Autonomous Quad-Equations Admitting, as Generalized Symmetries, Known Five-Point Differential-Difference Equations”, J. Nonlinear Math. Phys., 26:3 (2019), 333–357
Rustem N. Garifullin, Ravil I. Yamilov, “Integrable Modifications of the Ito–Narita–Bogoyavlensky Equation”, SIGMA, 15 (2019), 062, 15 pp.
Ufa Math. J., 11:3 (2019), 99–108
Garifullin R.N. Yamilov R.I. Levi D., “Non-invertible transformations of differential–difference equations”, J. Phys. A-Math. Theor., 49:37 (2016), 37LT01
R N Garifullin, I T Habibullin, R I Yamilov, “Peculiar symmetry structure of some known discrete nonautonomous equations”, J. Phys. A: Math. Theor., 48:23 (2015), 235201
Sergey Ya. Startsev, “Non-Point Invertible Transformations and Integrability of Partial Difference Equations”, SIGMA, 10 (2014), 066, 13 pp.
S. Ya. Startsev, “Integriruemye po Darbu differentsialno-raznostnye uravneniya, dopuskayuschie integral pervogo poryadka”, Ufimsk. matem. zhurn., 4:3 (2012), 161–176
S. Ya. Startsev, “Necessary conditions of Darboux integrability for differential-difference equations of a special kind”, Ufa Math. J., 3:1 (2011), 78–82
V. E. Adler, A. B. Shabat, “Dressing chain for the acoustic spectral problem”, Theoret. and Math. Phys., 149:1 (2006), 1324–1337
Yamilov, R, “Symmetries as integrability criteria for differential difference equations”, Journal of Physics A-Mathematical and General, 39:45 (2006), R541