New exact solutions of (3 + 1)‐dimensional generalized Kadomtsev‐Petviashvili equation using a combination of lie symmetry and singular manifold methods
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6031
Abstract: 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… read more here.
Keywords: lie symmetry; equation; singular manifold; symmetry singular ... See more keywords
A comprehensive analysis of Fokas–Lenells equation using Lie symmetry method
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DOI: 10.1002/mma.9892
Abstract: This article extracts analytical solutions of the Fokas–Lenells equation describing pulse propagation in optical fibers and presents a comprehensive analysis of the analytical solutions. This paper focuses on deriving analytical, non‐perturbative solutions for the Fokas–Lenells… read more here.
Keywords: lenells equation; fokas lenells; using lie; lie symmetry ... See more keywords
Lie symmetry analysis and invariant solutions of $$\varvec{(3+1)}$$(3+1)-dimensional Calogero–Bogoyavlenskii–Schiff equation
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DOI: 10.1007/s11071-018-4196-z
Abstract: Lie group analysis is applied to carry out the similarity reductions of the $$(3+1)$$(3+1)-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) equation. We obtain generators of infinitesimal transformations of the CBS equation and each of these generators depend on various… read more here.
Keywords: cbs equation; dimensional calogero; calogero bogoyavlenskii; lie symmetry ... See more keywords
Lie symmetry analysis, multiple exp-function method and conservation laws for the (2+1)-dimensional Boussinesq equation
Sign Up to like & getrecommendations! Published in 2024 at "Optical and Quantum Electronics"
DOI: 10.1007/s11082-024-06339-1
Abstract: In this study, we take into account the (2 + 1)-dimensional Boussinesq equation, a nonlinear evolution partial differential equation that describes how gravity waves move across the surface of the ocean. The symmetry reductions and… read more here.
Keywords: equation; method; dimensional boussinesq; boussinesq equation ... See more keywords
Lie Symmetry Analysis, Power Series Solutions and Conservation Laws of (2+1)-Dimensional Time Fractional Modified Bogoyavlenskii–Schiff Equations
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DOI: 10.1007/s44198-024-00195-z
Abstract: In this paper, Lie symmetry analysis method is applied to the (2+1)-dimensional time fractional modified Bogoyavlenskii–Schiff equations, which is an important model in physics. The one-dimensional optimal system composed by the obtained Lie symmetries is… read more here.
Keywords: symmetry analysis; dimensional time; power series; lie symmetry ... See more keywords
Generalized Lie symmetry analysis for non-linear differential equations: A purely viscous fluid model
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DOI: 10.1016/j.rinp.2017.09.020
Abstract: Abstract Prime objective of present study is to provide procedure in obtaining symmetries for mixed convection flow of viscous fluid due to an inclined porous stretching sheet. Two cases of stretching velocity namely power law… read more here.
Keywords: analysis; symmetry analysis; lie symmetry; viscous fluid ... See more keywords
Some more closed-form invariant solutions and dynamical behavior of multiple solitons for the (2+1)-dimensional rdDym equation using the Lie symmetry approach
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DOI: 10.1016/j.rinp.2021.104201
Abstract: Abstract The present study is devoted to obtaining some exact generalized solutions and new solitary wave solutions for a (2+1)-dimensional nonlinear r th dispersionless Dym (rdDym) equation by utilizing the Lie symmetry analysis. The Lie… read more here.
Keywords: closed form; solitons parabolic; lie symmetry; symmetry ... See more keywords
Lie symmetry methods for local volatility models
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DOI: 10.1016/j.spa.2019.10.009
Abstract: Abstract We investigate PDEs of the form u t = 1 2 σ 2 ( t , x ) u x x − g ( x ) u which are associated with the calculation of… read more here.
Keywords: volatility; volatility models; lie symmetry; symmetry methods ... See more keywords
Lie symmetry analysis and solitary wave solution of biofilm model Allen-Cahn
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DOI: 10.1038/s41598-024-62315-5
Abstract: The investigation presented in this study delves into the analysis of Lie symmetries for the bistable Allen-Cahn (BAC) equation with a quartic potential, specifically applied to the biofilm model. By employing the Lie symmetry method,… read more here.
Keywords: biofilm model; solitary wave; model; allen cahn ... See more keywords
Lie symmetry analysis and soliton solutions for complex short pulse equation
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DOI: 10.1080/17455030.2020.1807074
Abstract: The current study is dedicated for operating the Lie symmetry approach, to complex short pulse equation. The method reduces the complex short pulse equation to a system of ordinary differential equ... read more here.
Keywords: complex short; lie symmetry; short pulse; pulse equation ... See more keywords
Lie symmetry reductions, abound exact solutions and localized wave structures of solitons for a (2 + 1)-dimensional Bogoyavlenskii equation
Sign Up to like & getrecommendations! Published in 2021 at "Modern Physics Letters B"
DOI: 10.1142/s0217984921502523
Abstract: By applying the two efficient mathematical methods particularly with regard to the classical Lie symmetry approach and generalized exponential rational function method, numerous exact solutions are constructed for a (2 + 1)-dimensional Bogoyavlenskii equation, which… read more here.
Keywords: symmetry reductions; bogoyavlenskii equation; lie symmetry; symmetry ... See more keywords