Liu, Hanze; Li, Jibin; Zhang, Quanxin Lie symmetry analysis and exact explicit solutions for general Burgers’ equation. (English) Zbl 1166.35033 J. Comput. Appl. Math. 228, No. 1, 1-9 (2009). Summary: The Lie symmetry analysis is performed for the general Burgers’ equation. The exact solutions and similarity reductions generated from the symmetry transformations are provided. Furthermore, the all exact explicit solutions and similarity reductions based on the Lie group method are obtained, some new method and techniques are employed simultaneously. Such exact explicit solutions and similarity reductions are important in both applications and the theory of nonlinear science. Cited in 44 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35Q35 PDEs in connection with fluid mechanics 35C10 Series solutions to PDEs 22E70 Applications of Lie groups to the sciences; explicit representations Keywords:general Burgers’ equation; Lie symmetry analysis; similarity reduction; exact solution PDF BibTeX XML Cite \textit{H. Liu} et al., J. Comput. Appl. Math. 228, No. 1, 1--9 (2009; Zbl 1166.35033) Full Text: DOI OpenURL References: [1] Gardner, C.S.; Greene, J.M.; Kruskal, M.D.; Miura, R.M., Method for solving the korteweg – de Vries equation, Phys. rev. lett., 19, 1095-1097, (1967) · Zbl 1061.35520 [2] Li, Y.S., Soliton and integrable systems, (), (in Chinese) [3] Hirota, R.; Satsuma, J., A variety of nonlinear network equations generated from the Bäcklund transformation for the tota lattice, Suppl. prog. theor. phys., 59, 64-100, (1976) [4] Olver, P.J., Applications of Lie groups to differential equations, () · Zbl 0591.73024 [5] Bluman, G.W.; Kumei, S., Symmetries and differential equations, (1989), Springer-Verlag, World Publishing Corp. · Zbl 0718.35003 [6] Cantwell, B.J., Introduction to symmetry analysis, (2002), Cambridge University Press · Zbl 1082.34001 [7] Clarkson, P.; Kruskal, M., New similarity reductions of the Boussinesq equation, J. math. phys., 30, 10, 2201-2213, (1989) · Zbl 0698.35137 [8] Clarkson, P., New similarity reductions for the modified Boussinesq equation, J. phys. A: gen., 22, 2355-2367, (1989) · Zbl 0704.35116 [9] Craddock, M.; Platen, E., Symmety group methods for fundamental solutions, J. differential equations, 207, 285-302, (2004) · Zbl 1065.35016 [10] Craddock, M.; Lennox, K., Lie group symmetries as integral transforms of fundamental solutions, J. differential equations, 232, 652-674, (2007) · Zbl 1147.35009 [11] Liu, H.; Qiu, F., Analytic solutions of an iterative equation with first order derivative, Ann. differential equations, 21, 3, 337-342, (2005) · Zbl 1090.34600 [12] Liu, H.; Li, W., Discussion on the analytic solutions of the second-order iterative differential equation, Bull. Korean math. soc., 43, 4, 791-804, (2006) · Zbl 1131.34048 [13] Liu, H.; Li, W., The exact analytic solutions of a nonlinear differential iterative equation, Nonlinear anal., (2007) [14] Asmar, N.H., Partial differential equations with Fourier series and boundary value problems, (2005), China Machine Press Beijing [15] Rudin, W., Principles of mathematical analysis, (2004), China Machine Press Beijing, 223-228 [16] Fichtenholz, G.M., Functional series, (1970), Gordon & Breach New York, London, Paris · Zbl 0213.35001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.