On a new method for constructing exact solutions of the nonlinear differential equations of mathematical physics

Journal of Physics A: Mathematical and General

Volumn 31, Issue 21, 1998, Pages 4899-4907

  Barannyk, A F ^a   Yuryk, I I ^a  

^a INSTITUTE OF MATHEMATICS   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032577228     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/31/21/008     Document Type: Article

References (14)

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2. Olver P 1986 Applications of Lie Groups to Differential Equations (New York: Springer)
3. Fushchych W I, Shtelen V M and Serov N I 1993 Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Dordrecht: Kluwer)
4. Fushchych W I and Nikitin A G 1987 Symmetries of Maxwell's Equations (Dordrecht: Reidel)
5. Fushchych W I and Tsyfra I M 1987 On a reduction and solutions of nonlinear wave equations with broken symmetry J. Phys. A: Math. Gen. 20 L45-8
6. Levi D and Winternitz P 1989 J. Phys. A: Math. Gen. 22 2915-24
7. Fushchych W I and Barannyk A F 1996 A new method of constructing exact solutions of the nonlinear wave equations Dopovidi Natsi Akad. Nauk Ukrainy (Reports of the Natl Acad. Sci. Ukraine) N10, pp 48-51 (in Ukrainian)
8. Grundland A M, Harnad J and Winternitz P 1984 Symmetry reduction for nonlinear relativistically invariant equations J. Math Phys. 25 791-806
9. Cieciura G and Grundland A 1984 A certain class of solutions of the nonlinear wave equations J. Math. Phys. 25 3460-9
10. Fushchych W I, Barannyk L F and Barannyk A F 1991 Subgroup Analysis of Galilei and Poincaré Groups, and Reduction of Nonlinear Equations (Kiev: Naukova Dumka) (in Russian)
11. Collins C B 1976 Complex potential equations. I. A technique for solutions Proc. Camb. Phil. Soc. 9 225-36
12. Fushchych W I and Zhdanov R Z 1992 Nonlinear Spinor Equations: Symmetry and Exact Solutions (Kiev: Naukova Dumka) (in Russian)
13. Smirnov V I and Sobolev S L 1932 New method for solving a plane problem of elastic oscillations Proc. of the Seismological Institute of the Academy of Sciences USSR vol 20, pp 37-42
14. Smirnov V I and Sobolev S L 1933 On application of a new method to the study of elastic oscillations in a space with the axial symmetry Proc. of the Seismological Institute of the Academy of Sciences USSR vol 29, pp 43-51