Nonlinear Dynamics

, Volume 94, Issue 4, pp 2469–2477 | Cite as

Painlevé analysis and invariant solutions of generalized fifth-order nonlinear integrable equation

  • Lakhveer Kaur
  • Abdul-Majid Wazwaz
Original Paper


In present work, new form of generalized fifth-order nonlinear integrable equation has been investigated by locating movable critical points with aid of Painlevé analysis and it has been found that this equation passes Painlevé test for \(\alpha =\beta \) which implies affirmation toward the complete integrability. Lie symmetry analysis is implemented to obtain the infinitesimals of the group of transformations of underlying equation, which has been further pre-owned to furnish reduced ordinary differential equations. These are then used to establish new abundant exact group-invariant solutions involving various arbitrary constants in a uniform manner.


Generalized fifth-order nonlinear integrable equation Painlevé analysis Lie symmetry analysis Invariant solutions Generalized \(\left( \frac{G'}{G}\right) \)-expansion 


Compliance with ethical standards

Conflict of interest

We declare that we have no conflict of interest.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of MathematicsJaypee Institute of Information TechnologyNoidaIndia
  2. 2.Department of MathematicsSaint Xavier UniversityChicagoUSA

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