## 32 Citations

On the integrability conditions for a family of Liénard-type equations

- Mathematics
- 2016

We study a family of Liénard-type equations. Such equations are used for the description of various processes in physics, mechanics and biology and also appear as travelingwave reductions of some…

On the integrability of Liénard I-type equations via λ-symmetries and solvable structures

- MathematicsAppl. Math. Comput.
- 2018

Integrability Properties of Cubic Liénard Oscillators with Linear Damping

- MathematicsSymmetry
- 2019

It is demonstrated that the equations under consideration have a generalized Darboux first integral of a certain form if and only if they are linearizable.

Integrable Nonautonomous Liénard-Type Equations

- MathematicsTheoretical and Mathematical Physics
- 2018

We study a family of nonautonomous generalized Liénard-type equations. We consider the equivalence problem via the generalized Sundman transformations between this family of equations and type-I…

On the Integrability of Liénard Equations

- Mathematics
- 2019

A simple condition for integrability of Lienard equations is established to compute their general solution explicitly or by quadrature via a nonlocal transformation.

Nonlocal deformations of autonomous invariant curves for Liénard equations with quadratic damping

- MathematicsChaos, Solitons & Fractals
- 2021

## References

SHOWING 1-10 OF 28 REFERENCES

On the connection of the quadratic Lienard equation with an equation for the elliptic functions

- Mathematics
- 2015

The quadratic Lienard equation is widely used in many applications. A connection between this equation and a linear second-order differential equation has been discussed. Here we show that the whole…

A class of exact solutions of the Liénard-type ordinary nonlinear differential equation

- Mathematics
- 2014

A class of exact solutions is obtained for the Liénard-type ordinary nonlinear differential equation. As a first step in our study, the second-order Liénard-type equation is transformed into a first…

A conservation law for a generalized chemical Fisher equation

- MathematicsJournal of Mathematical Chemistry
- 2014

In this work we study a generalized Fisher equation with variable coefficients from the point of view of the theory of symmetry reductions in partial differential equations. There is a widespread…

On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations

- MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2005

A method for finding general solutions of second-order nonlinear ordinary differential equations by extending the Prelle–Singer (PS) method is briefly discussed. We explore integrating factors,…

Nonlinear self-adjointness and conservation laws for a generalized Fisher equation

- MathematicsCommun. Nonlinear Sci. Numer. Simul.
- 2013

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

- Mathematics
- 2009

In this second of the set of two papers on Lie symmetry analysis of a class of Lienard-type equation of the form x+f(x)x+g(x)=0, where overdot denotes differentiation with respect to time and f(x)…

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

- Mathematics
- 2009

We carry out a detailed Lie point symmetry group classification of the Lienard-type equation, x+f(x)x+g(x)=0, where f(x) and g(x) are arbitrary smooth functions of x. We divide our analysis into two…

Integrable Dissipative Nonlinear Second Order Differential Equations Via Factorizations and Abel Equations

- Mathematics
- 2018

We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order di fferential equations and the Abel equations which in its first kind form have…

Painleve analysis of the generalized Burgers-Huxley equation

- Mathematics
- 1990

A complete Painleve test (1900) is applied to the generalized Burgers-Huxley equation using the version of the Painleve analysis recently developed by Weiss, Tabor and Carnevale (1983) for partial…