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

2018 ◽  
Vol 94 (4) ◽  
pp. 2469-2477 ◽  
Author(s):  
Lakhveer Kaur ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Integrable Equation ◽  
Painlevé Analysis ◽  
Invariant Solutions ◽  
Nonlinear Integrable Equation ◽  
Fifth Order ◽  
Painleve Analysis

scholarly journals An optimal system of group-invariant solutions and conserved quantities of a nonlinear fifth-order integrable equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 829-841
Author(s):  
Innocent Simbanefayi ◽  
Chaudry Masood Khalique
Keyword(s):  
Nonlinear Partial Differential Equation ◽  
Group Analysis ◽  
Integrable Equation ◽  
Optimal System ◽  
Integral Approach ◽  
Conserved Quantities ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Group Invariant Solutions ◽  
Fifth Order

Abstract In this work, we perform Lie group analysis on a fifth-order integrable nonlinear partial differential equation, which was recently introduced in the literature and contains two dispersive terms. We determine a one-parameter group of transformations, an optimal system of group invariant solutions, and derive the corresponding analytic solutions. Topological kink, periodic and power series solutions are obtained. The existence of a variational principle for the underlying equation is proven using Helmholtz conditions and, thereafter, both local and nonlocal conserved quantities are obtained by utilising Noether’s theorem and a homotopy integral approach.

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