Abstract
In this paper, the Lie symmetry analysis is performed for the Degasperis-Procesi equation. By taking the package Desolv in maple and Lie group method, the exact solutions from the symmetry transformations are provided. Such exact explicit solutions are important in both applications and the theory of nonlinear science.
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Gardner, C.S., Greene, J.M., Kruskal, M.D., Miura, R.M.: Method for solving the Kortewegde Vries equation. Phys. Rev. Lett. 19, 1095–1097 (1967)
Li, Y.S.: Soliton and integrable systems. In: Advanced Series in Nonlinear Science, Shanghai Scientific and Technological Education Publishing House, Shang Hai (1999) (in Chinese)
Hirota, R., Satsuma, J.: A variety of nonlinear network equations generated from the Backlund transformation for the Tota lattice. Suppl. Prog. Theor. Phys. 59, 64–100 (1976)
Misirli, E., Gurefe, Y.: Exact solutions of the Drinfel‘d-Sokolov-Wilson equation using the Exp-function method. APPl. Math. ComPut., 2623–2627 (2010)
Geng, X.G., Wu, L.H.: Commun. Darboux Transformation and Explicit Solutions for Drinfel‘d-Sokolov-Wilson equation. Theor. Phys., 1090–1096 (2010)
Craddock, M.: Fundamental solutions, transition densities and the integration of Lie symmetries. Differential Equations 246, 2538–2560 (2009)
Clarkson, P., Kruskal, M.: New similarity reductions of the Boussinesq equation. J. Math. Phys. 30(10), 2201–2213 (1989)
Clarkson, P.: New similarity reductions for the modified Boussinesq equation. J. Phys. A: Gen. 22, 2355–2367 (1989)
Lixin, T., Lu, S.: Singular solitons of generalized Camassa-Holm models. Chaos, Solitons and Fraetals 32(2), 780–799 (2007)
Vu, K.T., Butcher, J., Carminati, J.: Similarity solutions of partial differential equations using DESOLV. Computer Physics Communicatios (2007)
Hereman, W., et al.: Direct methods and symbolic software for conservation laws of nonlinear equations. Advances in Nonlinear Waves and Symbolic Computation, 19–78 (2009)
Liu, H., Li, J.B., Zhang, Q.: Lie symmetry analysis and exact explicit solutions for general Burgers’ equation. Journal of Computational and Applied Mathematics (2008)
Liu, H., Li, J.B.: Lie group classifications and exact solutions for two variable-coefficient equation. Applied Mathematics and Computation, 2927–2935 (2009)
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Wang, Q., Wang, T. (2012). Lie Symmetry Analysis for the Degasperis-Procesi Equation Based on Maple. In: Liu, C., Wang, L., Yang, A. (eds) Information Computing and Applications. ICICA 2012. Communications in Computer and Information Science, vol 308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34041-3_42
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DOI: https://doi.org/10.1007/978-3-642-34041-3_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34040-6
Online ISBN: 978-3-642-34041-3
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