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A complete and partial integrability technique of the Lorenz system
Results in Physics, 2018 In this paper we deal with the well-known nonlinear Lorenz system that describes the deterministic chaos phenomenon. We consider an interesting problem with time-varying phenomena in quantum optics. Then we establish from the motion equations the passage
Lazhar Bougoffa +2 more
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Exact Travelling-Wave Solutions of the Extended Fifth-Order Korteweg-de Vries Equation via Simple Equations Method (SEsM): The Case of Two Simple Equations [PDF]
Entropy, 2022 We apply the Simple Equations Method (SEsM) for obtaining exact travelling-wave solutions of the extended fifth-order Korteweg-de Vries (KdV) equation. We present the solution of this equation as a composite function of two functions of two independent ...
Elena V. Nikolova
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Abel fractional differential equations using Variation of parameters method
Ratio Mathematica, 2022 The Variation of Parameters Method (VPM) is utilized throughout the research to identify a numerical model for a nonlinear fractional Abel differential equation (FADE).
Nithya Devi, P. Prakash
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Generalized symmetries, first integrals, and exact solutions of chains of differential equations [PDF]
Open Communications in Nonlinear Mathematical Physics, 2021 New integrability properties of a family of sequences of ordinary differential equations, which contains the Riccati and Abel chains as the most simple sequences, are studied.
C. Muriel, M. C. Nucci
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Advances in Mathematical Physics, 2022 The (2+1)-dimensional Lax integrable equation is decomposed into solvable ordinary differential equations with the help of known (1+1)-dimensional soliton equations associated with the Ablowitz-Kaup-Newell-Segur soliton hierarchy.
Xiaohong Chen
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Properties of inversion operator of the Abel matrix equation
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2010 Generalization of integral-differential Riemann-Liouville operator on the matrix order-is reviewed and its properties are studied. Theorem of the composition of operators of the matrix of integration and differentiation can be proved.
Rina R Ismagilova
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Isotropic Perfect Fluids in Modified Gravity
Universe, 2023 We generate the Einstein–Gauss–Bonnet field equations in higher dimensions for a spherically symmetric static spacetime. The matter distribution is a neutral fluid with isotropic pressure.
Shavani Naicker +2 more
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Partial Differential Equations in Applied Mathematics, 2020 A particular function defined in terms of the Lambert function W is shown to serve as the basis for exact traveling wave solutions to several reaction–diffusion–convection (RDC) equations involving rational, non-linear diffusion terms. These represent a
Brian Wesley Williams
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Charged fluids in higher order gravity
European Physical Journal C: Particles and Fields, 2023 We generate the field equations for a charged gravitating perfect fluid in Einstein–Gauss–Bonnet gravity for all spacetime dimensions. The spacetime is static and spherically symmetric which gives rise to the charged condition of pressure isotropy that ...
Shavani Naicker +2 more
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Using Abel\u27s Theorem to Explain Repeated Roots of the Characteristic Equation [PDF]
, 2011 This document describes how one can derive the solutions to a linear constant coefficient homogeneous differential equation with repeated roots in the characteristic equation with Abel\u27s ...
Green, William
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