Factorization technique and isochronous condition for coupled quadratic and mixed Liénard-type nonlinear systems

[1]  M. Nucci,et al.  Noether symmetries and the quantization of a Liénard-type nonlinear oscillator , 2013, Journal of Nonlinear Mathematical Physics.

[2]  M. Lakshmanan,et al.  Lie point symmetries classification of the mixed Liénard-type equation , 2015 .

[3]  M. C. Nucci,et al.  Quantization of quadratic Li\'enard-type equations by preserving Noether symmetries , 2014, 1406.0192.

[4]  M. Lakshmanan,et al.  Erratum: “Classification of Lie point symmetries for quadratic Liénard type equation ẍ+f(x)ẋ2+g(x)=0” [J. Math. Phys. 54, 053506 (2013)] , 2014 .

[5]  M. Lakshmanan,et al.  On the complete Lie point symmetries classification of the mixed quadratic-linear Li$\acute{\textbf{e}}$nard type equation $\ddot{x}+f(x)\dot{x}^2+g(x)\dot{x}+h(x)=0$ , 2014, 1402.3407.

[6]  M. Lakshmanan,et al.  Classification of Lie point symmetries for quadratic Li$\acute{\textbf{e}}$nard type equation $\ddot{x}+f(x)\dot{x}^2+g(x)=0$ , 2013, 1302.0350.

[7]  V. K. Chandrasekar,et al.  On the complete integrability of a nonlinear oscillator from group theoretical perspective , 2012, 1207.4945.

[8]  Exact solutions of coupled Liénard-type nonlinear systems using factorization technique , 2012, 1201.5931.

[9]  J. Strelcyn,et al.  Isochronicity conditions for some planar polynomial systems II , 2011 .

[10]  J. L. Romero,et al.  First integrals, integrating factors and λ-symmetries of second-order differential equations , 2009 .

[11]  J. Strelcyn,et al.  Isochronicity conditions for some planar polynomial systems , 2009, 1005.5048.

[12]  V. K. Chandrasekar,et al.  Nonstandard conserved Hamiltonian structures in dissipative/damped systems: Nonlinear generalizations of damped harmonic oscillator , 2009 .

[13]  M. Lakshmanan,et al.  On the complete integrability and linearization of nonlinear ordinary differential equations. V. Linearization of coupled second-order equations , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[14]  Zdzislaw E. Musielak,et al.  Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients , 2008 .

[15]  V. K. Chandrasekar,et al.  On the complete integrability and linearization of nonlinear ordinary differential equations. IV. Coupled second-order equations , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[16]  Hongbo Li,et al.  Single and multi-solitary wave solutions to a class of nonlinear evolution equations , 2008 .

[17]  Z E Musielak Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients , 2008 .

[18]  M Berkovich Lev,et al.  METHOD OF FACTORIZATION OF ORDINARY DIFFERENTIAL OPERATORS AND SOME OF ITS APPLICATIONS , 2007 .

[19]  H. Rosu,et al.  Traveling-Wave Solutions for Korteweg–de Vries–Burgers Equations through Factorizations , 2006, math-ph/0604004.

[20]  M Senthilvelan,et al.  On the complete integrability and linearization of nonlinear ordinary differential equations. II. Third-order equations , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[21]  H. Rosu,et al.  Riccati-parameter solutions of nonlinear second-order ODEs , 2005, math-ph/0510072.

[22]  H. Rosu,et al.  Nonlinear Second Order Ode's: Factorizations and Particular Solutions , 2005, math-ph/0504055.

[23]  H. Rosu,et al.  Supersymmetric pairing of kinks for polynomial nonlinearities. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  B. Mielnik,et al.  Factorization: little or great algorithm? , 2004 .

[25]  A. Chouikha Isochronous centers of Lienard type equations and applications , 2004, math/0410022.

[26]  J. Cariñena,et al.  One-dimensional model of a quantum nonlinear harmonic oscillator , 2004, hep-th/0501106.

[27]  M. Senthilvelan,et al.  A non-linear oscillator with quasi-harmonic behaviour: two- and n-dimensional oscillators , 2004, math-ph/0406002.

[28]  M. Sabatini On the period function of x″+f(x)x′2+g(x)=0 , 2004 .

[29]  E. Kamke Differentialgleichungen : Lösungsmethoden und Lösungen , 1977 .

[30]  M. Lakshmanan,et al.  On a unique nonlinear oscillator , 1974 .

[31]  T. E. Hull,et al.  The factorization method , 1951 .