References
- D. Acemoglu, Introduction to modern economic growth (Levine’s Bibliography), Department of Economics, UCLA, 2007.
- R.J. Barro and X.I. Sala-i-Martin, Economic growth, The MIT press, Cambridge, 2004.
- G. Bauman, Symmetry analysis of differential equations using MathLie, Springer-Verlag, New York, 2000.
- G.W. Bluman and S.C. Anco, Symmetries and integration methods for differential equations, Springer-Verlag, New York, 1993.
- G.W. Bluman and S.C. Anco, Integrating factors and first integrals for ordinary differential equations, Eur. J. Appl. Math. 9 (1998), 245–259. doi: 10.1017/S0956792598003477
- V.K. Chandrasekar, M. Senthilvelan, and M. Lakshmanan, Extended Prelle-Singer Method and Integrability/Solvability of a Class of Nonlinear n th Order Ordinary Differential Equations, J. Math. Phys. 12 (2005), 184–201.
- V.K. Chandrasekar, M. Senthilvelan, and M. Lakshmanan, On the complete integrability and linearization of nonlinear ordinary differential equations, part III: coupled first order equations, Proc. R. Soc. Lond. Ser. A 465 (2009), 585–608.
- V.K. Chandrasekar, M. Senthilvelan, and M. Lakshmanan, On the complete integrability and linearization of nonlinear ordinary differential equations, Part III: Coupled first order equations, Proc. R. Soc. Lond. Ser. A 465 (2009), 585–608.
- A. Cheviakov, GeM software package for computation of symmetries and conservation laws of differential equations, Comp. Phys. Comm. 176 (2007), 48–61. doi: 10.1016/j.cpc.2006.08.001
- G. Darboux, Mémoire sur les équations différentielles algébriques du premier ordre et du premier degré, Bull. Sci. Math. 2 (1878), 60–96, 123–144, 151–200.
- R. Dorfman, An economic interpretation of optimal control theory, The American Economic Review (AER) 59(5) (1969), 817–831.
- G. Gün Polat and T. Özer, On analysis of nonlinear dynamical systems via methods connected with λ-symmetry, Nonlinear Dyn. 85(3) (2016), 1571–1595. doi: 10.1007/s11071-016-2780-7
- G. Gün Polat and T. Özer, New conservation laws, Lagrangian forms and exact solutions of modified-Emden equation, ASME J. Comput. Nonlin. Dyn. 12(4) (2017), 041001. doi: 10.1115/1.4035408
- G. Gün Polat and T. Özer, On Group-Theoretical Analysis of Nonlinear Optimal Control Problems with Hamiltonian Formalism, J. Nonlinear Math. Phys. 27(1) (2020), 106–129. doi: 10.1080/14029251.2020.1683985
- G. Gün Polat and T. Özer, On Ramsey Dynamical Model and Closed-Form Solution, J. Non-linear Math. Phys. 28(2) (2021), 209–218. doi: 10.2991/jnmp.k.210103.001
- C.G.J. Jacobi, Sul principio dellultimo moltiplicatore, e suo come nuovo principio generale di meccanica, Giornale Arcadico di Scienze Lettere ed Arti 99 (1844), 129–146.
- S. Kumar and S. Rani, Invariance analysis, optimal system, closed-form solutions and dynamical wave structures of a (2+1)-dimensional dissipative long wave system, Physica Scripta 96(12) (2021), 125202. doi: 10.1088/1402-4896/ac1990
- S. Kumar and S. Rani, Symmetries of optimal system, various closed-form solutions, and propagation of different wave profiles for the Boussinesq-Burgers system in ocean waves, Physics of Fluids 34 (2022), 037109. doi: 10.1063/5.0085927
- A.A. LeKama and K. Schubert, A note on the consequences of an endogenous discounting depending on the environmental quality, Macroecon. Dyn. 11(2) (2007), 272–289. doi: 10.1017/S1365100507060063
- R. Lucas, On the Mechanics of Economic Development, J. Monet. Econ. 22(1) (1988), 3–42. doi: 10.1016/0304-3932(88)90168-7
- Mohanasubha, R., Chandrasekar, V.K., Senthilvelan, M., Lakshmanan, M., Interplay of symmetries, null forms, Darbou polynomials, integrating factors and Jacobi multipliers in integrable second-order differential equations, Proc. R. Soc. A 470(2163) (2014), 20130656. doi: 10.1098/rspa.2013.0656
- R. Mohanasubha, M. Senthilvelan, and M. Lakshmanan, On the interconnections between various analytic approaches in coupled first-order nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simulat. 62 (2018), 213–228. doi: 10.1016/j.cnsns.2018.02.021
- C. Muriel and J.L. Romero, New methods of reduction for ordinary differential equations, IMA J. Appl. Math. 66(2) (2001), 111–125. doi: 10.1093/imamat/66.2.111
- C. Muriel and J.L. Romero, First integrals, integrating factors and symmetries of second order differential equations, J. Phys. A: Math. Theor. 42(36) (2009), 365207. doi: 10.1088/1751-8113/42/36/365207
- R. Naz, The applications of the partial Hamiltonian approach to mechanics and other areas, Int. J. Non. Linear Mech. 86(1) (2016), 1–6. doi: 10.1016/j.ijnonlinmec.2016.07.009
- R. Naz, F.M. Mahomed, and A. Chaudhry, A partial Hamiltonian approach for current value Hamiltonian systems, Commun. Nonlinear Sci. Numer. Simul. 19(10) (2014), 3600–3610. doi: 10.1016/j.cnsns.2014.03.023
- R. Naz, F.M. Mahomed, and A. Chaudhry, A partial Lagrangian method for dynamical systems, Nonlinear Dyn. 84(3) (2016), 1783–1794. doi: 10.1007/s11071-016-2605-8
- R. Naz, F.M. Mahomed, and A. Chaudhry, Closed-form solutions for the Lucas-Uzawa model of economic growth via the partial Hamiltonian approach, Commun. Nonlinear Sci. Numer. Simul. 30(1–3) (2016), 299–306. doi: 10.1016/j.cnsns.2015.06.033
- M.C. Nucci, Jacobi Last Multiplier and Lie symmetries: A Novel Application of an Old Relationship, J. Nonlinear Math. Phys. 12(2) (2005), 284–304. doi: 10.2991/jnmp.2005.12.2.9
- M.C. Nucci, Seeking (and Finding) Lagrangians, Theoretical and Mathematical Physics 160(1) (2009), 1014–1021. doi: 10.1007/s11232-009-0092-5
- P.J. Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, 1993.
- M. Prelle and M. Singer, Elementary First Integrals of Differential Equations, Trans. Am. Math. Soc. 279(1) (1983), 215–229. doi: 10.1090/S0002-9947-1983-0704611-X
- F. Ramsey, A Mathematical theory of saving, Economic Journal 38 (1928), 543–559. doi: 10.2307/2224098
- S. Rani, S. Kumar, and R. Kumar, Invariance analysis for determining the closed-form solutions, optimal system, and various wave profiles for a (2+1)-dimensional weakly coupled B-Type Kadomtsev-Petviashvili equations, Journal of Ocean Engineering and Science 11(2) (2022), https://doi.org/10.1016/j.joes.2021.12.007