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Linked References

1. W.-X. Ma, X. Gu, and L. Gao, “A note on exact solutions to linear differential equations by the matrix exponential,” Advances in Applied Mathematics and Mechanics, vol. 1, no. 4, pp. 573–580, 2009.
2. S. lie, “Vorlesungen Über Differentialgleichungen mit Bekannten Infinitesinalen Transformationen,” BG Teubner, 1891.
3. A. G. Johnpillai and C. M. Khalique, “Lie group classification and invariant solutions of mKdV equation with time-dependent coefficients,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1207–1215, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
4. W.-X. Ma and M. Chen, “Do symmetry constraints yield exact solutions?” Chaos, Solitons & Fractals, vol. 32, no. 4, pp. 1513–1517, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
5. M. L. Gandarias and M. S. Bruzon, “Classical and nonclassical symmetries of a generalized Boussinesq equation,” Journal of Nonlinear Mathematical Physics, vol. 5, no. 1, pp. 8–12, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
6. J. Y. Dong, S. C. Xu, and Z. X. Chen, “On permutation symmetries of hopfield model neural network,” Discrete Dynamics in Nature and Society, vol. 6, no. 2, pp. 129–136, 2001.
7. W. X. Ma, R. K. Bullough, P. J. Caudrey, and W. I. Fushchych, “Time-dependent symmetries of variable-coefficient evolution equations and graded Lie algebras,” Journal of Physics A, vol. 30, no. 14, pp. 5141–5149, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
8. W.-X. Ma and Z.-X. Zhou, “Coupled integrable systems associated with a polynomial spectral problem and their Virasoro symmetry algebras,” Progress of Theoretical Physics, vol. 96, no. 2, pp. 449–457, 1996. View at Publisher · View at Google Scholar
9. W.-X. Ma and M. Chen, “Direct search for exact solutions to the nonlinear Schrödinger equation,” Applied Mathematics and Computation, vol. 215, no. 8, pp. 2835–2842, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
10. P. E. Hydon, “Discrete point symmetries of ordinary differential equations,” The Royal Society of London. Proceedings A, vol. 454, no. 1975, pp. 1961–1972, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
11. P. E. Hydon, “How to construct the discrete symmetries of partial differential equations,” European Journal of Applied Mathematics, vol. 11, no. 5, pp. 515–527, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
12. W. X. Ma, “A hierarchy of coupled Burgers systems possessing a hereditary structure,” Journal of Physics A, vol. 26, no. 22, pp. L1169–L1174, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
13. M. Nadjafikhah and R. Bakhshandeh-Chamazkoti, “Symmetry group classification for general Burgers' equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 9, pp. 2303–2310, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
14. A. Ouhadan and E. H. El Kinani, “Lie symmetries of the equation $u_t(x,t)+g(u)u_x(x,t)=0$,” Advances in Applied Clifford Algebras, vol. 17, no. 1, pp. 95–106, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
15. M. Nadjafikhah, “Lie symmetries of inviscid Burgers' equation,” Advances in Applied Clifford Algebras, vol. 19, no. 1, pp. 101–112, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
16. M. Nadjafikhah, “Classification of similarity solutions for inviscid Burgers' equation,” Advances in Applied Clifford Algebras, vol. 20, no. 1, pp. 71–77, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
17. I. L. Freire, “Note on Lie point symmetries of Burgers Equations,” Anais do CNMAC, 2009.
18. M. A. Abdulwahhab, A. H. Bokhari, A. H. Kara, and F. D. Zaman, “On the Lie point symmetry analysis and solutions of the inviscid Burgers equation,” Pramana Journal of Physics, vol. 77, pp. 407–414, 2011.
19. L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, NY, USA, 1982.
20. P. J. Olver, Applications of Lie Groups to Differential Equations, vol. 107, Springer, New York, NY, USA, 1993. View at Publisher · View at Google Scholar
21. G. W. Bluman and S. Kumei, Symmetries and Differential Equations, vol. 81, Springer, New York, NY, USA, 1989.