On the integrability of non-polynomial scalar evolution equations

Journal of Differential Equations

Volumn 166, Issue 1, 2000, Pages 132-150

  Sanders, Jan A ^a   Wang, Jing Ping ^b  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Evolution equation; Generalized symmetry; Integrability

Indexed keywords

EID: 35748966843     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1006/jdeq.2000.3782     Document Type: Article

References (20)

1. F. Beukers, On a sequence of polynomials, J. Pure Appl. Algebra 117/118 (1997), 97-103; "Algorithms for Algebra," Eindhoven, 1996.
2. F. Beukers, "Algorithms for Algebra," Eindhoven, 1996.
3. A. H. Bilge, On the equivalence of linearization and formal symmetries as integrability tests for evolution equations, J. Phys. A 26, No. 24 (1993), 7511-7519.
4. L. J. Billera, R. Cushman, and J. A. Sanders, The Stanley decomposition of the harmonic oscillator, Nederl. Akad. Wetensch. Indag. Math. 50, No. 4 (1988), 375-393.
5. F. Boulier, D. Lazard, F. Ollivier, and M. Petitot, Representation for the radical of a finitely generated differential ideal, in "Proceedings of ISSAC'95, Montréal, Canada, 1995," pp. 158-166.
6. F. Boulier, D. Lazard, F. Ollivier, and M. Petitot, Computing representations for radicals of finitely generated differential ideals, technical report, Ref. IT-306, Université Lille I, 59655, Villeneuve d'Ascq, France, 1997, submitted for publication.
7. B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt, "Maple V Language Reference Manual," Springer-Verlag, Berlin, 1991.
8. I. Dorfman, "Dirac Structures and Integrability of Nonlinear Evolution Equations," Wiley, Chichester, 1993.
9. V. G. Drinfel'd, S. I. Svinolupov, and V. V. Sokolov, Classification of fifth-order evolution equations having an infinite series of conservation laws, Dokl. Akad. Nauk Ukrain. SSR Ser. A 10 (1985), 8-10.
10. A. S. Fokas, A symmetry approach to exactly solvable evolution equations, J. Math. Phys. 21, No. 6 (1980), 1318-1325.
11. A. Mawla, "Finding Symmetries of λ-Homogeneous Scalar Evolution Equations Using Maple, Form, and Perl," Master's thesis, Vrije Universiteit, Amsterdam, 1998.
12. A. V. Mikhaĭlov, A. B. Shabat, and V. V. Sokolov, The symmetry approach to classifica-tion of integrable equations, in "What Is Integrability?," Springer Series on Nonlinear Dynamics, pp. 115-184, Springer-Verlag, Berlin, 1991.
13. P. J. Olver, "Applications of Lie Groups to Differential Equations," Graduate Texts in Mathematics, Vol. 107, 2nd ed., Springer-Verlag, New York, 1993.
14. P. J. Olver and V. V. Sokolov, Integrable evolution equations on associative algebras, Comm. Math. Phys. 193, No. 2 (1998), 245-268.
15. P. J. Olver and J. P. Wang, Classification of integrable one-component systems on associative algebras, technical report, UMN, 1999.
16. J. A. Sanders and J. P. Wang, Combining Maple and Form to decide on integrability questions, Comput. Phys. Comm. 115, Nos. 2/3 (1998), 447-459.
17. J. A. Sanders and J. P. Wang, On the integrability of homogeneous scalar evolution equations, J. Differential Equations 147, No. 2 (1998), 410-434.
18. J. A. M. Vermaseren, "Symbolic Manipulation with FORM, Tutorial and Reference Manual," CAN, Amsterdam, 1991.
19. J. P. Wang, "Symmetries and Conservation Laws of Evolution Equations," Ph. D. thesis, Vrije Universiteit, Amsterdam, 1998.
20. F. P. M. Wetzels, "Computing Conditions on Symmetries of Evolution Equations," Master's thesis, Vrije Universiteit, Amsterdam, 1998.