Abstract
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, 1993.
A.S. Fokas, Symmetries and integrability, Stud. Appl. Math. 77: 3 (1987), 253–299.
M. Blaszak, Multi-Hamiltonian Theory of Dynamical Systems, Springer-Verlag, Heildelberg, 1998.
B. Fuchssteiner, Mastersymmetries, higher order time-dependent symmetries and conserved densities of nonlinear evolution equations, Progr. Theor. Phys. 70 (1983), 1508–1522.
W. Oevel, A geometrical approach to integrable systems admitting time dependent invariants, in Topics in Soliton Theory and Exactly Solvable Nonlinear Equations (Oberwolfach, 1986) (M. Ablowitz, B. Fuchssteiner, M. Kruskal, eds.), World Scientific Publishing, Singapore, 1987, pp. 108–124.
V.V. Sokolov, On the symmetries of evolution equations, Russ. Math. Surveys 43: 5 (1988), 165–204.
P.J. Olver, V.V. Sokolov, Integrable evolution equations on associative algebras, Comm. Math. Phys. 193 (1998), 245–268.
J.A. Sanders and J.P. Wang, On the integrability of homogeneous scalar evolution equations, J. Differential Equations, 147 (1998), 410–434.
A.H. Bilge, On the equivalence of linearization and formal symmetries as integrability tests for evolution equations, J. Phys. A: Math. Gen. 26 (1993), 7511–7519.
J.P. Wang, Symmetries and Conservation Laws of Evolution Equations, Ph.D. Thesis, Vrije Universiteit van Amsterdam, 1998.
A.V. Mikhailov, A.B. Shabat, and R.I. Yamilov, The symmetry approach to classification of nonlinear equations. Complete lists of integrable systems, Russ. Math. Surveys 42:4 (1987), 1–63.
A.V. Mikhailov, A.B. Shabat and V.V. Sokolov, The symmetry approach to classification of integrable equations, in What is Integrability? (V.E. Zakharov, ed.), Springer-Verlag, New York, 1991, pp. 115–184.
A.V. Mikhailov, R.I. Yamilov, Towards classification of (2+I)-dimensional integrable equations. Integrability conditions. I, J. Phys. A: Math. Gen. 31 (1998), 6707–6715.
N.H. Ibragimov, Transformation Groups Applied to Mathematical Physics, D. Reidel Publishing Co., Boston, 1985.
F.Kh. Mukminov, V.V. Sokolov, Integrable evolution equations with constraints, Mat. Sb.(N.S.) 133(175):3 (1987), 392–414.
V.V. Sokolov, T. Wolf, A symmetry test for quasilinear coupled systems, Inverse Problems 15 (1999), L5–L11.
M.V. Foursov, Classification of certain type integrable coupled potential KdV and modified KdV-type equations, J. Math. Phys. 41 (2000), 6173–6185.
B. Fuchssteiner, Integrable nonlinear evolution equations with time-dependent coefficients, J. Math. Phys. 34 (1993), 5140–5158.
I. Dorfman, Dirac Structures and Integrability of Nonlinear Evolution Equations, John Wiley & Sons, Chichester, 1993.
Symmetries and Conservation Laws for Differential Equations of Mathematical Physics (I.S. Krasil’shchik and A.M. Vinogradov, eds.), American Mathematical Society, Providence, 1999.
J.A. Cavalcante and K. Tenenblat, Conservation laws for nonlinear evolution equations, J. Math. Phys. 29 (1988), 1044–1049.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Sergyeyev, A. (2001). Time Dependence and (Non)commutativity of Symmetries of Evolution Equations. In: Duplij, S., Wess, J. (eds) Noncommutative Structures in Mathematics and Physics. NATO Science Series, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0836-5_31
Download citation
DOI: https://doi.org/10.1007/978-94-010-0836-5_31
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-6999-8
Online ISBN: 978-94-010-0836-5
eBook Packages: Springer Book Archive