On the criteria for integrability of the Liénard equation
Tài liệu tham khảo
Liénard, 1928, Étude des oscillations entreténues, Rev. Gen. Electr., 23, 901
Liénard, 1928, Étude des oscillations entreténues, Rev. Gen. Electr., 23, 946
Zaitsev, 2002
Guckenheimer, 1983
Lakshmanan, 2003
Andronov, 2011
Chandrasekar, 2005, On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations, Proc. R. Soc. A Math. Phys. Eng. Sci., 461, 2451, 10.1098/rspa.2005.1465
Frenkel, 2009, Traveling solitary waves for doubly-resonant media: Computation via simulated annealing, Appl. Math. Lett., 22, 1112, 10.1016/j.aml.2008.11.009
Gandarias, 2013, Nonlinear self-adjointness and conservation laws for a generalized Fisher equation, Commun. Nonlinear Sci. Numer. Simul., 18, 1600, 10.1016/j.cnsns.2012.11.023
Kudryashov, 2014, A note on solutions of the generalized Fisher equation, Appl. Math. Lett., 32, 53, 10.1016/j.aml.2014.02.009
Rosa, 2015, A conservation law for a generalized chemical Fisher equation, J. Math. Chem., 53, 941, 10.1007/s10910-014-0451-9
Johnson, 1970, A non-linear equation incorporating damping and dispersion, J. Fluid Mech., 42, 49, 10.1017/S0022112070001064
Kudryashov, 2009, On “new travelling wave solutions” of the KdV and the KdV–Burgers equations, Commun. Nonlinear Sci. Numer. Simul., 14, 1891, 10.1016/j.cnsns.2008.09.020
Polyanin, 2011
Estevez, 1990, Painleve analysis of the generalized Burgers–Huxley equation, J. Phys. A. Math. Gen., 23, 4831, 10.1088/0305-4470/23/21/023
Yefimova, 2004, Exact solutions of the Burgers–Huxley equation, J. Appl. Math. Mech., 68, 413, 10.1016/S0021-8928(04)00055-3
Pandey, 2009, A group theoretical identification of integrable cases of the Liénard-type equation ẍ+f(x)ẋ+g(x)=0. I. Equations having nonmaximal number of Lie point symmetries, J. Math. Phys., 50
Pandey, 2009, A group theoretical identification of integrable equations in the Liénard-type equation ẍ+f(x)ẋ+g(x)=0. II. Equations having maximal Lie point symmetries, J. Math. Phys., 50
Mancas, 2013, Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations, Phys. Lett. A., 377, 1434, 10.1016/j.physleta.2013.04.024
Harko, 2014, A class of exact solutions of the Liénard-type ordinary nonlinear differential equation, J. Eng. Math., 89, 193, 10.1007/s10665-014-9696-3
Nakpim, 2010, Linearization of second-order ordinary differential equations by generalized Sundman transformations, symmetry, Integr. Geom. Methods Appl., 6, 1
Kudryashov, 2014, Analytical solutions of the Rayleigh equation for empty and gas-filled bubble, J. Phys. A Math. Theor., 47, 10.1088/1751-8113/47/40/405202
Kudryashov, 2015, Analytical solutions for problems of bubble dynamics, Phys. Lett. A., 379, 798, 10.1016/j.physleta.2014.12.049
Kudryashov, 2015, On the connection of the quadratic Liénard equation with an equation for the elliptic functions, Regul. Chaotic Dyn., 20, 486, 10.1134/S1560354715040073
Nakpim, 2010, Linearization of third-order ordinary differential equations by generalized Sundman transformations: The case X‴+αX=0, Commun. Nonlinear Sci. Numer. Simul., 15, 1717, 10.1016/j.cnsns.2009.06.020
Moyo, 2011, Application of the generalised Sundman transformation to the linearisation of two second-order ordinary differential equations, J. Nonlinear Math. Phys., 18, 213, 10.1142/S1402925111001386
Ince, 1956
