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Potential symmetries and conservation laws for generalized quasilinear hyperbolic equations. (English) Zbl 1242.35177
Summary: Based on the Lie group method, the potential symmetries and invariant solutions for generalized quasilinear hyperbolic equations are studied. To obtain the invariant solutions in an explicit form, the physically interesting situations with potential symmetries are focused on, and the conservation laws for these equations in three physically interesting cases are found by using the partial Lagrangian approach.
MSC:
35L72Quasilinear second-order hyperbolic equations
35B06Symmetries, invariants, etc. (PDE)
References:
[1]Olver, P. J. Applications of Lie Groups to Differential Equations, Springer, New York (1986)
[2]Ovsiannikov, L. V. Group Analysis of Differential Equations, Academic Press, New York (1982)
[3]Liu, N., Liu, X. Q., and Lü, H. L. New exact solutions and conservation laws of the (2+1)-dimensional dispersive long wave equations. Physics Letters A, 373(2), 214–220 (2009) · Zbl 1227.35124 · doi:10.1016/j.physleta.2008.11.007
[4]Ibragimov, N. H., Kara, A. H., and Mahomed, F. M. Lie-Bäcklund and Noether symmetries with applications. Nonlinear Dynamics, 15, 115–136 (1998) · Zbl 0912.35011 · doi:10.1023/A:1008240112483
[5]Yasar, E. and Özer, T. Conservation laws for one-layer shallow water waves systems. Nonlinear Analysis: Real World Applications, 11(2), 838–848 (2010) · Zbl 1184.35266 · doi:10.1016/j.nonrwa.2009.01.028
[6]Mei, F. X. Applications of Lie Groups and Lie Algebraic to Constraint Mechanical Systems (in Chinese), Science Press, Beijing (1999)
[7]Bluman, G. W., Reid, G. J., and Kumei, S. New classes of symmetries for partial differential equations. Journal of Mathematical Physics, 29, 806–811 (1988) · Zbl 0669.58037 · doi:10.1063/1.527974
[8]Khater, A. H., Callebaut, D. K., Abdul-Aziza, S. F., and Abdelhameeda, T. N. Potential symmetry and invariant solutions of Fokker-Planck equation modelling magnetic field diffusion in magnetohydrodynamics including the Hall current. Physica A: Statistical Mechanics and Its Applications, 341, 107–122 (2004) · doi:10.1016/j.physa.2004.04.118
[9]Bluman, G. W. Applications of Symmetry Methods to Partial Differential Equations, Springer, Berlin (2010)
[10]Noether, E. Invariante variations probleme. Nachrichten von der Könglichen Gesellschaft der Wissenschaften zu Göttingen, 1(3), 235–257 (1918)
[11]Bessel-Hagen, E. Über die erhaltungssätzeder elektrodynamik. Mathematische Annalen, 84, 258–276 (1921) · Zbl 02603184 · doi:10.1007/BF01459410
[12]Fu, J. L., Chen, L. Q., and Chen, B. Y. Noether-type theorem for discrete nonconservative dynamical systems with nonregular lattices. Science China: Physics, Mechanics and Astronomy, 53(3), 545–554 (2010) · doi:10.1007/s11433-009-0258-z
[13]Fu, J. L., Fu, H., and Liu, R. W. Hojman conserved quantities of discrete mechanico-electrical systems constructed by continuous symmetries. Physics Letters A, 374(17–18), 1812–1818 (2010) · Zbl 1236.78010 · doi:10.1016/j.physleta.2010.02.046
[14]Fu, J. L., Chen, L. Q., Jiménez, S., and Tang, Y. F. Non-Noether symmetries and Lutzky conserved quantities for mechanico-electrical systems. Physics Letters A, 358(1), 5–10 (2006) · Zbl 1142.70318 · doi:10.1016/j.physleta.2006.04.097
[15]Ibragimov, N. H. CRC Handbook of Lie Group Analysis of Differential Equations: Volume 1, CRC-Press, Boca Raton, Florida (1994)
[16]Khalique, C. M. and Mahomed, F. M. Conservation laws for equations related to soil water equations. Mathematical Problems in Engineering, 2005(1), 141–150 (2005) · Zbl 1079.35004 · doi:10.1155/MPE.2005.141
[17]Kara, A. H. and Mahomed, F. M. Noether-type symmetries and conservation laws via partial Lagrangians. Nonlinear Dynamics, 45(3), 367–383 (2006) · Zbl 1121.70014 · doi:10.1007/s11071-005-9013-9
[18]Johnpillai, A. G., Kara, A. H., and Mahomed, F. M. Conservation laws of a nonlinear (1 + 1) wave equation. Nonlinear Analysis: Real World Applications, 11(4), 2237–2242 (2010) · Zbl 1194.35272 · doi:10.1016/j.nonrwa.2009.06.013
[19]Bokharia, A. H., Al-Dweika, A. Y., Mahomed, F. M., and Zaman, F. D. Conservation laws of a nonlinear (n+1) wave equation. Nonlinear Analysis: Real World Applications, 11(4), 2862–2870 (2010) · Zbl 1197.35174 · doi:10.1016/j.nonrwa.2009.10.009
[20]Qin, M. C., Mei, F. X., and Xu, X. J. Nonclassical potential symmetries and invariant solutions of the heat equation. Applied Mathematics and Mechanics (English Edition), 27(2), 247–253 (2006) DOI 10.1007/s10483-006-0213-y · Zbl 1167.35306 · doi:10.1007/s10483-006-0213-y
[21]Bluman, G. W., Temuerchaolu, and Sahadevan, R. Local and nonlocal symmetries for nonlinear telegraph equations. Journal of Mathematical Physics, 46(2), 023505 (2005) · Zbl 1076.35077 · doi:10.1063/1.1841481