New exact solutions of (3 + 1)‐dimensional generalized Kadomtsev‐Petviashvili equation using a combination of lie symmetry and singular manifold methods

A new combination of Lie symmetry and Singular Manifold methods has been employed to study (3 + 1)‐dimensional generalized Kadomtsev‐Petviashvili (KP). Infinite‐dimensional space of Lie vectors has been established. Single and dual linear combinations of Lie vectors are used after appropriate calcul...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2020-03, Vol.43 (4), p.2045-2055
Main Authors: Saleh, Rasha, Rashed, Ahmed S.
Format: Article
Language:English
Subjects:
Differential equations
Eigenvectors
Exact solutions
generalized Kadomtsev‐Petviashvili equation
Lie infinitesimals
Mathematical analysis
Ordinary differential equations
Schwarzian derivative
singular manifolds method
Symmetry
Vectors (mathematics)
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Summary:A new combination of Lie symmetry and Singular Manifold methods has been employed to study (3 + 1)‐dimensional generalized Kadomtsev‐Petviashvili (KP). Infinite‐dimensional space of Lie vectors has been established. Single and dual linear combinations of Lie vectors are used after appropriate calculations of the arbitrary functions to reduce the equation to an ordinary differential equation (ODE). The resulting ODE is then analytically solved through the singular manifold method which resulted in a Bäcklund truncated series with seminal analysis leading to a Schwarzian differential equation in the Eigenfunction φ (η). Solving this differential equation leads to new analytical solutions.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6031