TY - JOUR AU - Nyirenda, Darlison AU - Folly-Gbetoula, Mensah PY - 2017 TI - Invariance analysis and exact solutions of some sixth-order difference equations JO - Journal of Nonlinear Sciences and Applications SP - 6262--6273 VL - 10 IS - 12 AB - We perform a full Lie point symmetry analysis of difference equations of the form \[ u_{n+6}=\frac{u_nu_{n+4}}{u_{n+2}(A _n + B _n u_nu_{n+4})}\ , \] where the initial conditions are non-zero real numbers. Consequently, we obtain four non-trivial symmetries. Eventually, we get solutions of the difference equation for random sequences \((A_n)\) and \((B_n)\). This work is a generalization of a recent result by Khaliq and Elsayed [A. Khaliq, E. M. Elsayed, J. Nonlinear Sci. Appl., \({\bf 9}\) (2016), 1052--1063]. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.12.11 DO - 10.22436/jnsa.010.12.11 ID - Nyirenda2017 ER - TY - JOUR TI - Periodicity and solutions for some systems of nonlinear rational difference equations AU - E. M. Elsayed AU - T. F. Ibrahim JO - Hacet. J. Math. Stat. PY - 2015 DA - 2015// VL - 44 ID - Elsayed2015 ER - TY - JOUR TI - Exact traveling-wave solutions for linear and nonlinear heat-transfer equations AU - G. Feng AU - X.-J. Yang AU - H. M. Srivasta JO - Therm. Sci. PY - 2016 DA - 2016// VL - 00 ID - Feng2016 ER - TY - JOUR TI - Symmetry, reductions and exact solutions of the difference equation \(u_{n+2} = au_n/(1+bu_nu_{n+1})\) AU - M. Folly-Gbetoula JO - J. Difference Equ. Appl. PY - 2017 DA - 2017// VL - 23 ID - Folly-Gbetoula 2017 ER - TY - JOUR TI - Symmetries, conservation laws, and ‘integrability’ of difference equations AU - M. Folly-Gbetoula AU - A. H. Kara JO - Adv. Difference Equ. PY - 2014 DA - 2014// VL - 2014 ID - Folly-Gbetoula2014 ER - TY - JOUR TI - Symmetries and first integrals of ordinary difference equations AU - P. E. Hydon JO - R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. PY - 2000 DA - 2000// VL - 456 ID - Hydon2000 ER - TY - BOOK TI - Difference equations by differential equation methods AU - P. E. Hydon PB - Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press PY - 2014 DA - 2014// CY - Cambridge ID - Hydon2014 ER - TY - JOUR TI - Solving a class of three-order max-type difference equations AU - T. F. Ibrahim JO - Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. PY - 2014 DA - 2014// VL - 21 ID - Ibrahim 2014 ER - TY - JOUR TI - Global stability of a higher-order difference equation AU - T. F. Ibrahim AU - M. A. El-Moneam JO - Iran. J. Sci. Technol. Trans. A Sci. PY - 2017 DA - 2017// VL - 41 ID - Ibrahim2017 ER - TY - JOUR TI - The dynamics and solution of some difference equations AU - A. Khaliq AU - E. M. Elsayed JO - J. Nonlinear Sci. Appl. PY - 2016 DA - 2016// VL - 9 ID - Khaliq2016 ER - TY - JOUR TI - Global behavior of an anti-competitive system of fourth-order rational difference equations AU - A. Q. Khan AU - Q. Din AU - M. N. Qureshi AU - T. F. Ibrahim JO - Comput. Ecol. Softw. PY - 2014 DA - 2014// VL - 4 ID - Khan2014 ER - TY - JOUR TI - Lie group formalism for difference equations AU - D. Levi AU - L. Vinet AU - P. Winternitz JO - J. Phys. A PY - 1997 DA - 1997// VL - 30 ID - Levi1997 ER - TY - JOUR TI - Classification und Integration von gewhnlichen Differentialgleichungen zwischen xy, die eine Gruppe von Transformationen gestatten AU - S. Lie JO - (German) Math. Ann. PY - 1888 DA - 1888// VL - 22 ID - Lie 1888 ER - TY - JOUR TI - Soliton solutions, conservation laws, and reductions of certain classes of nonlinearwave equations AU - R. Morris AU - A. H. Kara AU - A. Chowdhury AU - A. Biswas JO - Z. Naturforsch. A PY - 2012 DA - 2012// VL - 67 ID - Morris2012 ER - TY - JOUR TI - Invariante variationsprobleme AU - E. Noether JO - (German) Nachr. D. König. Gesellsch. D. Wiss. Zu Göttingen, Math-phys. Klasse PY - 1918 DA - 1918// VL - 1918 ID - Noether1918 ER - TY - JOUR TI - Lie symmetries and the integration of difference equations AU - G. R. W. Quispel AU - R. Sahadevan JO - Phys. Lett. A PY - 1993 DA - 1993// VL - 184 ID - Quispel1993 ER - TY - JOUR TI - Generalizations of Noether’s theorem in classical mechanics AU - W. Sarlet AU - F. Cantrijn JO - SIAM Rev. PY - 1981 DA - 1981// VL - 23 ID - Sarlet1981 ER - TY - JOUR TI - Exact traveling wave solutions for the local fractional two-dimensional Burgers-type equations AU - X.-J. Yang AU - F. Gao AU - H. M. Srivastava JO - Comput. Math. Appl. PY - 2017 DA - 2017// VL - 73 ID - Yang2017 ER - TY - JOUR TI - Exact traveling-wave solution for local fractional Boussinesq equation in fractal domain AU - X.-J. Yang AU - J. A. Tenreiro Machado AU - D. Baleanu JO - Fractals PY - 2017 DA - 2017// VL - 25 ID - Yang2017 ER - TY - JOUR TI - On exact traveling-wave solutions for local fractional Korteweg-de Vries equation AU - X.-J. Yang AU - J. A. Tenreiro Machado AU - D. Baleanu AU - C. Cattani JO - Chaos PY - 2016 DA - 2016// VL - 26 ID - Yang2016 ER -