Nonlinear superposition principles obtained by Lie symmetry methods

Journal of Mathematical Analysis and Applications

Volumn 214, Issue 2, 1997, Pages 633-657

  Goard, Joanna M ^a   Broadbridge, Philip ^a  

^a UNIVERSITY OF WOLLONGONG   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; COMPUTATIONAL METHODS; MATHEMATICAL PROGRAMMING; NONLINEAR EQUATIONS; PROBLEM SOLVING;

LIE SYMMETRY ALGEBRA; NONLINEAR SUPERPOSITION METHODS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0031249674     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5604     Document Type: Article

References (10)

1. 1. R. L. Andersen and N. H. Ibragimov, "Lie-Bäcklund Transformations in Applications," SIAM Studies in Applied Mathematics, SIAM, Philadelphia, 1979.
2. 2. G. W. Bluman and S. Kumei, "Symmetries and Differential Equations," Springer-Verlag, New York, 1989.
3. 3. A. Inselberg, Noncommutative superpositions for nonlinear operators, J. Math. Anal. Appl. 29 (1970), 294-298.
4. 4. S. E. Jones and W. F. Ames, Nonlinear superposition, J. Math. Anal. Appl. 17 (1967), 484-487.
5. 5. P. H. M. Kersten, "Infinitesimal Symmetries: A Computational Approach," Centrum voor Wiskunde en Informatica, Amsterdam, 1987.
6. 6. G. L. Lamb, Analytical descriptions of ultrashort optical pulse propagation in a resonant medium, Rev. Mod. Phys. 43 (1971), 99-124.
7. 7. S. A. Levin, Principles of nonlinear superposition, J. Math. Anal. Appl. 30 (1970), 197-205.
8. 8. F. Schwarz, Symmetries of differential equations: from Sophus Lie to computer algebra, SIAM Rev. 30 (1988), 450-481.
9. 9. J. Sherring, "Dimsym Users Manual," La Trobe University, Melbourne, 1993.
10. 10. M. N. Spijker, Superposition in linear and nonlinear ordinary differential equations, J. Math. Anal. Appl. 30 (1970), 206-222.