×

zbMATH — the first resource for mathematics

Bäcklund transformations for hereditary symmetries. (English) Zbl 0491.35007

MSC:
35A30 Geometric theory, characteristics, transformations in context of PDEs
35L65 Hyperbolic conservation laws
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Olver, P.J., Evolution equations possessing infinitely many symmetries, J. math. phys., 18, 1212-1215, (1977) · Zbl 0348.35024
[2] Pirani, F.A.E.; Robinson, D.C.; Shadwick, W.F., Local jet bundle formulation of Bäcklund transformations, () · Zbl 0427.58003
[3] Fokas, A.S.; Anderson, R.L., Group theoretical nature of Bäcklund transformations, Lett. math. phys., 3, 117-126, (1979) · Zbl 0417.35006
[4] Fuchssteiner, B., Application of hereditary symmetries to nonlinear evolution equations, Nonlinear analysis, TMA, 3, 849-862, (1979) · Zbl 0419.35049
[5] Yamamuro, S., Differential calculus in topological linear spaces, Lecture notes in mathematics, 374, (1974), Berlin-Heidelberg-New York · Zbl 0276.58001
[6] Fokas, A.S., A symmetry approach to exactly solvable evolution equations, J. math. phys., 21, 1318-1325, (1980) · Zbl 0455.35109
[7] Fuchssteiner, B., Pure soliton solutions of some nonlinear partial differential equations, Comm. math. phys., 55, 187-194, (1977) · Zbl 0361.35018
[8] \scFuchssteiner B., Application of spectral-gradient methods to nonlinear soliton equations (Preprint).
[9] Miura, R.M., Korteweg-de Vries equation and generalizations. I: A remarkable explicit nonlinear transformation, J. math. phys., 9, 1202-1204, (1968) · Zbl 0283.35018
[10] Cole, J.D., On a quasi-linear parabolic equation occuring in aerodynamics, Q. appl. math., 9, 225-236, (1951) · Zbl 0043.09902
[11] Hopf, E., The equation ut+uux=uxx, Communs pure appl. math., 3, 201-230, (1950)
[12] Fokas, A.S., Invariants, (), Ph.D. Thesis · Zbl 0432.70027
[13] Yortsos, Y.C.; Fokas, A.S., An analytical solution for linear waterflood including the effects of capillary pressure, Spe 9407, (1980)
[14] Fuchssteiner, B., Comparison of the two-soliton collision for several nonlinear evolution equations, Lett. math. phys., 4, 177-183, (1980) · Zbl 0458.35089
[15] Fokas, A.S.; Fuchssteiner, B., On the structure of symplectic operators and hereditary symmetries, Lettere al nuovo cimento, 28, 299, (1980)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.