Painlevé analysis and invariant solutions of generalized fifth-order nonlinear integrable equation. (English) Zbl 1422.37047
Summary: 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.
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
Keywords:
generalized fifth-order nonlinear integrable equation; Painlevé analysis; Lie symmetry analysis; invariant solutions; generalized \(\left(\frac{G'}{G}\right) \)-expansionReferences:
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