Dym equation: group analysis and conservation laws

[1] D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional calculus, vol. 3 of Series on Complexity, Nonlinearity and Chaos, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012. Models and numerical methods.

[2] G. W. Bluman and S. C. Anco, Symmetry and integration methods for differential equations, vol. 154 of Applied Mathematical Sciences, Springer-Verlag, New York, 2002.

[3] G. W. Bluman, A. F. Cheviakov, and S. C. Anco, Applications of symmetry methods to partial differential equations, vol. 168 of Applied Mathematical Sciences, Springer, New York, 2010.

[4] E. F. Doungmo Goufo, S. Kumar, and S. B. Mugisha, Similarities in a fifth-order evolution equation with and with no singular kernel, Chaos Solitons Fractals, 130 (2020), pp. 109467, 7.

[5] F. Gesztesy and K. Unterkofler, Isospectral deformations for Sturm-Liouville and Dirac-type operators and associated nonlinear evolution equations, Rep. Math. Phys., 31 (1992), pp. 113–137.

[6] B. Ghanbari, S. Kumar, and R. Kumar, A study of behaviour for immune and tumor cells in immuno[1]genetic tumour model with non-singular fractional derivative, Chaos Solitons Fractals, 133 (2020), pp. 109619, 11.

[7] N. Habibi, E. Lashkarian, E. Dastranj, and S. R. Hejazi, Lie symmetry analysis, conservation laws and numerical approximations of time-fractional Fokker-Planck equations for special stochastic process in foreign exchange markets, Phys. A, 513 (2019), pp. 750–766.

[8] S. R. Hejazi and E. Lashkarian, Lie group analysis and conservation laws for the time-fractional third order KdV-type equation with a small perturbation parameter, J. Geom. Phys., 157 (2020), pp. 103830, 10.

[9] S. R. Hejazi, E. Saberi, and F. Mohammadizadeh, Anisotropic non-linear time-fractional diffusion equation with a source term: classification via Lie point symmetries, analytic solutions and numerical simulation, Appl. Math. Comput., 391 (2021), pp. Paper No. 125652, 21.

[10] P. E. Hydon, Symmetry methods for differential equations, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2000. A beginner’s guide.

[11] N. Ibragimov, Nonlinear self-adjointness in constructing conservation laws, in Archives of ALGA, vol. 7/8, 2010, pp. 1–99.

[12] A. H. Kara and F. M. Mahomed, Noether-type symmetries and conservation laws via partial Lagrangians, Nonlinear Dynam., 45 (2006), pp. 367–383.

[13] M. Kruskal, Nonlinear wave equations, in Dynamical systems, theory and applications (Rencontres, Battelle Res. Inst., Seattle, Wash., 1974), 1975, pp. 310–354. Lecture Notes in Phys., Vol. 38.

[14] S. Kumar, A new analytical modelling for fractional telegraph equation via Laplace transform, Appl. Math. Model., 38 (2014), pp. 3154–3163.

[15] S. Kumar, A. Ahmadian, R. Kumar, D. Kumar, J. Singh, D. Baleanu, and M. Salimi, An efficient numerical method for fractional sir epidemic model of infectious disease by using bernstein wavelets, Mathematics, 8 (2020), p. 558.

[16] S. Kumar, S. Ghosh, R. Kumar, and M. Jleli, A fractional model for population dynamics of two interacting species by using spectral and Hermite wavelets methods, Numer. Methods Partial Differential Equations, 37 (2021), pp. 1652–1672.

[17] S. Kumar, S. Ghosh, B. Samet, and E. F. D. Goufo, An analysis for heat equations arises in diffusion process using new Yang-Abdel-Aty-Cattani fractional operator, Math. Methods Appl. Sci., 43 (2020), pp. 6062– 6080.

[18] S. Kumar, R. Kumar, R. P. Agarwal, and B. Samet, A study of fractional Lotka-Volterra popula[1]tion model using Haar wavelet and Adams-Bashforth-Moulton methods, Math. Methods Appl. Sci., 43 (2020), pp. 5564–5578.

[19] S. Kumar, R. Kumar, C. Cattani, and B. Samet, Chaotic behaviour of fractional predator-prey dynamical system, Chaos Solitons Fractals, 135 (2020), pp. 109811, 12.

[20] S. Kumar, R. Kumar, M. S. Osman, and B. Samet, A wavelet based numerical scheme for fractional order SEIR epidemic of measles by using Genocchi polynomials, Numer. Methods Partial Differential Equations, 37 (2021), pp. 1250–1268.

[21] E. Lashkarian and S. R. Hejazi, Polynomial and non-polynomial solutions set for wave equation using Lie point symmetries, Comput. Methods Differ. Equ., 4 (2016), pp. 298–308.

[22] E. Lashkarian, E. Saberi, and S. Reza Hejazi, Symmetry reductions and exact solutions for a class of nonlinear PDEs, Asian-Eur. J. Math., 9 (2016), pp. 1650061, 11.

[23] F. Mohammadizadeh, S. Rashidi, and S. R. Hejazi, Space-time fractional Klein-Gordon equation: symmetry analysis, conservation laws and numerical approximations, Math. Comput. Simulation, 188 (2021), pp. 476–497.

[24] R. Mokhtari, Exact solutions of the Harry-Dym equation, Commun. Theor. Phys. (Beijing), 55 (2011), pp. 204–208.

[25] A. Naderifard, S. R. Hejazi, and E. Dastranj, Symmetry properties, conservation laws and exact solutions of time-fractional irrigation equation, Waves Random Complex Media, 29 (2019), pp. 178–194.

[26] M. Nadjafikhah and P. Kabi-Nejad, Approximate symmetries of the harry dym equation, International Scholarly Research Notices, 2013 (2013).

[27] P. J. Olver, Applications of Lie groups to differential equations, vol. 107 of Graduate Texts in Mathematics, Springer-Verlag, New York, second ed., 1993.

[28]__ , Equivalence, invariants, and symmetry, Cambridge University Press, Cambridge, 1995.

[29] S. Rashidi and S. Reza Hejazi, Symmetry properties, similarity reduction and exact solutions of fractional Boussinesq equation, Int. J. Geom. Methods Mod. Phys., 14 (2017), pp. 1750083, 15.

[30] S. Reza Hejazi and S. Rashidi, Symmetries, conservation laws and exact solutions of the time-fractional diffusivity equation via Riemann-Liouville and Caputo derivatives, Waves Random Complex Media, 31 (2021), pp. 690–711.

[31] E. Saberi and S. Reza Hejazi, A comparison of conservation laws of the Boussinesq system, Kragujevac J. Math., 43 (2019), pp. 173–200.

[32] E. Saberi, S. Reza Hejazi, and A. Motamednezhad, Lie symmetry analysis, conservation laws and similarity reductions of Newell-Whitehead-Segel equation of fractional order, J. Geom. Phys., 135 (2019), pp. 116– 128.

[33] P. Veeresha, D. Prakasha, and S. Kumar, A fractional model for propagation of classical optical solitons by using nonsingular derivative, Mathematical Methods in the Applied Sciences, (2020).

[34] G. Wang, A. Kara, E. Buhe, and K. Fakhar, Group analysis and conservation laws of a coupled system of partial differential equations describing the carbon nanotubes conveying fluid, Romanian Journal in physics, 60 (2015), pp. 952–960.

[35] G. Wang, A. H. Kara, and K. Fakhar, Symmetry analysis and conservation laws for the class of timefractional nonlinear dispersive equation, Nonlinear Dynam., 82 (2015), pp. 281