[1] H. Liu, J. Li, L. Liu, Lie group classifications and exact solutions for two variable-coefficient equations, Applied Mathematics and Computation, 215 (2009), 2927-2935.
[2] C. Gardner et al, Method for solving the Korteweg-de Vries equation, Phys. Rev. Lett., 19 (1967), 1095-1097.
[3] Y. Li, Soliton and integrable systems, Advanced Series in Nonlinear Science, Shanghai Scientific and Technological Education Publishing House, Shanghai, 1999 (in Chinese).
[4] R. Liu, Compatibility method application in the evolution equation with variable coefficients, Journal of Hebei Normal University, Natural science edition, Hebei, 2011 (in Chinese).
[5] R. Hirota, J. Satsuma, A variety of nonlinear network equations generated from the B¨acklund transformation for the Tota lattice, Suppl. Prog. Theor. Phys., 59 (1976), 64-100.
[6] H. Liu, et al., Exact periodic wave solutions for the hKdV equation, Nonlinear Anal., (2008).
[7] P. Clarkson, M. Kruskal, New similarity reductions of the Boussinesq equation, J. Math. Phys., 30 (1989), 2201-2213.
[8] P. Clarkson, New similarity reductions for the modified Boussinesq equation, J. Phys. A: Gen., 22 (1989), 2355-2367.
[9] P. Olver, Applications of Lie Groups to Differential Equations, Grauate Texts in Mathematics, 107 (1993).
[10] G. Bluman, S. Kumei, Symmetries and Differential Equations, Springer-Verlag, (1989).
[11] B. Cantwell, Introduction to Symmetry Analysis, Cambridge University Press, (2002).
[12] H. Liu, et al., Lie symmetry analysis and exact explicit solutions for general Burgers’ equation, J. Comput. Appl. Math., (2008).
[13] M. Craddock, E. Platen, Symmety group methods for fundamental solutions, J. Differential Equations, 207 (2004), 285-302.
[14] M. Craddock, K. Lennox, Lie group symmetries as integral transforms of fundamental solutions, J. Differential Equations, 232 (2007), 652-674.
[15] S. Watanabe, M. Miyakawa, M. Tada, J. Phys. Soc. Jpn., 45 (1978), 2030.
[16] N. Saitoh, S. Watanabe, J. Phys. Soc. Jpn., 50 (1981), 1774.
[17] K. Muroya, S. Watanabe, J. Phys. Soc. Jpn., 50 (1981), 3159.
[18] S. Watanabe, M. Tada, J. Phys. Soc. Jpn., 50 (1981), 3443.
[19] K. Muroya, N. Saitoh, S. Watanabe, J. Phys. Soc. Jpn., 51 (1982), 1024.
[20] F. Kako, M. Miyakawa, S. Watanabe, J. Phys. Soc. Jpn., 55 (1986), 2919.
[21] M. Matsukawa, S. Watanabe, H. Tanaca, J. Phys. Soc. Jpn., 58 (1989), 3081.
[22] S. Ishiwata, S. Watanabe, H. Tanaca, J. Phys. Soc. Jpn., 59 (1990), 1163.
[23] Y. Okada, S. Watanabe, H. Tanaca, J. Phys. Soc. Jpn. 59 (1990), 2647.
[24] K. Kawamura, S. Watanabe, J. Phys. Soc. Jpn. 60 (1991), 82.
[25] Taogetusang, L. YI, New infinite sequence soliton-like solutions of nonlinear LC circuit equations, Journal of Inner Mongolia University, Natural science edition, Inner Mongolia, 46 (2015), 33-42 (in Chinese).
[26] Taogetusang, L. YI, Many new solutions of nonlinear LC circuit equation, Chinese Journal of Quantum Electronics, 32 (2015), 30-39 (in Chinese).
[27] H. Liu, et al., Lie symmetry analysis and exact solutions for the short pulse equation, Nonlinear Analysis, 71 (2009), 2126-2133.
[28] H. Liu, F. Qiu, Analytic solutions of an iterative equation with first order derivative, Ann. Differential Equations, 21 (2005), 337-342.
[29] H. Liu, W. Li, Discussion on the analytic solutions of the second-order iterative differential equation, Bull. Korean Math. Soc., 43 (2006), 791-804.
[30] H. Liu, W. Li, The exact analytic solutions of a nonlinear differential iterative equation, Nonlinear Anal, 69 (2008), 2466-2478.
[31] N. Asmar, Partial Differential Equations with Fourier Series and Boundary Value Problems, China Machine Press, 2005.
[32] Y. Shang, Y. Huang, Explicit and exact traveling wave solutions to the nonlinear LC circuit equation, Acta. Phys. Sin., 62 (2013), 1-9 (in Chinese). |