| GENERAL |
|
|
|
|
Group Classification and Exact Solutions of a Class of Variable Coefficient Nonlinear Wave Equations |
| HUANG Ding-Jiang1, MEI Jian-Qin2, ZHANG Hong-Qing2 |
| 1Department of Mathematics, East China University of Science and Technology, Shanghai 2002372Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 |
|
| Cite this article: |
|
HUANG Ding-Jiang, MEI Jian-Qin, ZHANG Hong-Qing 2009 Chin. Phys. Lett. 26 050202 |
|
|
|
|
Abstract Complete group classification of a class of variable coefficient (1+1)-dimensional wave equations is performed. The possible additional equivalence transformations between equations from the class under consideration and the conditional equivalence groups are also investigated. These allow simplification of the results of the classification and further applications of them. The derived Lie symmetries are used to construct exact solutions of special forms of these equations via the classical Lie method. Nonclassical symmetries of the wave equations are discussed.
|
| Keywords:
02.20.Sv
02.30.Jr
|
|
|
Received: 01 September 2008
Published: 23 April 2009
|
|
| PACS: |
02.20.Sv
|
(Lie algebras of Lie groups)
|
| |
02.30.Jr
|
(Partial differential equations)
|
|
|
|
|
|
[1] Ames W F 1972 Nonlinear Partial DifferentialEquations in Engineering (New York: Academic)
[2] Ames W F, Adams E and Lohner R J 1981 Int. J.Non-Linear Mech. 16 439
[3] Bluman G and Cheviakov A F 2007 J. Math. Anal. Appl. 333 93
[4] Bluman G W and Kumei S 1989 Symmetries andDifferential Equations (New York: Springer)
[5] Bluman G, Temuerchaolu and Sahadevan R 2005 J. Math.Phys. 46 023505
[6] Chikwendu S C 1981 Int. J. Non-Linear Mech. 16117
[7] Donato A 1987 Int. J. Non-Linear Mech. 22 307
[8] Gandarias M L, Torrisi M and Valenti A 2004 Int. J.Non-Linear Mech. 39 389
[9] Huang D J and Ivanova N M 2007 J. Math. Phys 48 073507 (23 pages)
[10] Ibragimov N H 1994 Lie Group Analysis ofDifferential Equations-Symmetries, Exact Solutions and ConservationLaws (Boca Raton, FL: CRC) vol 1
[11] Ibragimov N H, Torrisi M and Valenti A 1991 J. Math.Phys. 32 2988
[12] Kingston J G and Sophocleous C 1998 J. Phys. A:Math. Gen. 31 1597
[13] Lahno V, Zhdanov R and Magda O 2006 Acta Appl.Math. 91 253
[14] Lie S 1881 On Integration of a Class of LinearPartial Differential Equations by Means of Definite Integrals (CRCHandbook of Lie Group Analysis of Differential Equations) vol 2 pp473 (translation by Ibragimov N H of Arch. for Math., Bd. VI, Heft3, 328--368, Kristiania)
[15] Meleshko S V 1994 J. Appl. Math. Mech. 58 629
[16] Olver P J 1986 Application of Lie Groups toDifferential Equations (New York: Springer)
[17] Oron A and Rosenau P 1986 Phys. Lett. A 118172
[18] Ovsiannikov L V 1982 Group Analysis of DifferentialEquations (New York: Academic)
[19] Patera J and Winternitz P 1977 J. Math. Phys. 18 1449
[20] Popovych R O and Ivanova N M 2004 J. Phys. A: Math.Gen. 37 7547
[21] Pucci E 1987 Riv. Mat. Univ. Parma 12N4 71
[22] Pucci E and Salvatori M C 1986 Int. J. Non-LinearMech. 21 147
[23] Torrisi M and Valenti A 1985 Int. J. Non-LinearMech. 20 135
[24] Vaneeva O O, Johnpillai A G, Popovych R O and SophocleousC 2008 Appl. Math. Lett. 21 248
[24] Zhdanov R Z and Lahno V I 1998 Physica D: NonlinearPhenomena 122 178 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
