Symmetry Group Analysis of a Fifth-Order KdV Equation with Variable Coefficients

References

• Avdonina, E. D., Ibragimov, N. H. (2013). Conservation laws and exact solutions for nonlinear diffusion in anisotropic media. Commun. Nonlinear Sci. Numer. Simulat. 18:2595–2603.
   Google Scholar
• Anco, S. C., Bluman, G. (2002). Direct construction method for conservation laws of partial differential equations Part I: Examples of conservation law classifications. Euro. J Appl. Math. 13:545–566.
   Google Scholar
• Anco, S. C., Bluman, G. (2002). Direct construction method for conservation laws of partial differential equations Part II: General treatment. Euro. J. Appl. Math. 13:567–585.
   Google Scholar
• de la Rosa, R., Gandarias, M. L., Bruzón. (2016). Symmetries and conservation laws of a fifth-order KdV equation with time-dependent coefficients and linear damping. Nonlinear Dyn. 84:135–141.
   Google Scholar
• Freire, I. L. (2013). New classes of nonlinearly self-adjoint evolution equations of third- and fifth-order. Commun. Nonlinear Sci. Numer. Simulat. 18:493–499.
   Google Scholar
• Gandarias, M. L. (2011). Weak self-adjoint differential equations. J. Phys. A. 44:262001–262007.
   Google Scholar
• Gandarias, M. L., Bruzón, M. S. (2012). Some conservation laws for a forced KdV equation. Nonlinear Anal. Real World Appl. 13:2692–2700.
   Google Scholar
• Gandarias, M. L., Khalique, C. M. (2016). Symmetries, solutions and conservation laws of a class of nonlinear dispersive wave equations. Commun. Nonlinear Sci. Numer. Simulat. 32:114–121.
   Google Scholar
• Ibragimov, N. H. (2007). A new conservation theorem. J. Math. Anal. Appl. 333:311–328.
   Google Scholar
• Ibragimov, N. H. (2011). Nonlinear self-adjointness and conservation laws. J. Phys. A: Math. Theor. 44:432002–432010.
   Google Scholar
• Ibragimov, N. H., Khamitova, R., Avdonina, E. D., Galiakberova, L. R. (2015). Conservation laws and solutions of a quantum drift-diffusion model for semiconductors. Int. J. Non-Linear Mech. 77:69–73.
   Google Scholar
• Lee, C. T., Lee, C. C. (2012). Lax pairs and Hamiltonians for the Kaup-Kupershmidt-type equation. Phys. Scr. 85:035004 ( 5pp).
   Google Scholar
• Liu, Q., Zhu, J. M. (2006). Exact Jacobian elliptic function solutions and hyperbolic function solutions for Sawada-Kotere equation with variable coefficient. Phys. Lett. A. 352:233–238.
   Google Scholar
• Olver, P. (1993). Applications of Lie Groups to Differential Equations. New York: Springer-Verlag.
   Google Scholar
• Ovsyannikov, L. V. (1982). Group analysis of differential equations. New York: Academic.
   Google Scholar
• Pocheketa, O. A., Popovych, R. O., Vaneeva, O. O. (2014). Group classification and exact solutions of variable-coefficient generalized Burgers equations with linear damping. Appl. Math. Comput. 243:232–244.
   Google Scholar
• Qu, Q. X., Tian, B., Sun, K., Jiang, Y. (2011). Bäcklund transformation, Lax pair, and solutions for the Caudrey-Dodd-Gibbon equation. J. Math Phys. 52:013511.
   Google Scholar
• Senthilvelan, M., Torrisi, M., Valenti, A. (2006). Equivalence transformations and differential invariants of a generalized nonlinear Schrödinger equation. J. Phys. A: Math. Gen. 39:3703–3713.
   Google Scholar
• Tracinà, R., Bruzón, M. S., Gandarias, M. L., Torrisi, M. (2014). Nonlinear self-adjointness, conservation laws, exact solutions of a system of dispersive evolution equations. Commun. Nonlinear Sci Numer Simulat. 19:3036–3043.
   Google Scholar
• Triki, H., Wazwaz, A. M. (2014). Traveling wave solutions for fifth-order KdV type equations with time-dependent coefficients. Commun. Nonlinear Sci. Numer. Simulat. 19:404–408.
   Google Scholar
• Wolf, T. (1993). An efficiency improved program LIEPDE for determining Lie-symmetries of PDEs. Proceedings of Modern Group Analysis: Advances Analytical and Computational Methods in Mathematical Physics. 377–385.
   Google Scholar