In this paper, we present Lie symmetry analysis of a generalized (1+1)-dimensional porous medium equation characterized by parameters m and d. Through group classification, we examine how these parameters influence the Lie symmetry structure of the e...
As a powerful tool that can be used to solve both continuous and discrete equations, the Lie symmetry analysis of dynamical systems on a time scale is investigated. Applying the method to the Burgers equation and Euler equation, we get the symmetry o...
This paper studies a mixed PDE containing the second time derivative and a quadratic nonlinearity of the Monge–Ampère type in two spatial variables, which is encountered in geophysical fluid dynamics. The Lie group symmetry analysis of t...
The Guéant and Pu model of option pricing and hedging, which takes into account transaction costs, and the impact of operations on the market is studied by group analysis methods. The infinite-dimensional continuous group of equivalence transf...
This paper considers the Lie symmetry analysis of a class of fractional Zakharov-Kuznetsov equations. We systematically show the procedure to obtain the Lie point symmetries for the equation. Accordingly, we study the vector fields of this equation....
We consider a variable coefficient Burgers system in two spatial variables. A similarity mapping is used to reduce the number of independent variables. Lie symmetry analysis is applied to the reduced system. We present the equivalence groups for this...
The Boiti–Leon–Manna–Pempinelli (BLMP) equation with coefficients being functions of time is considered. Since the coefficient functions are arbitrary, we have a class of BLMP equations. Symmetry analysis is carried out for this cla...
In this paper we make a Lie symmetry analysis of a generalized nonlinear beam equation with both second-order and fourth-order wave terms, which is extended from the classical beam equation arising in the historical events of travelling wave behavior...
In this paper, we mainly put the Lie symmetry analysis method on the Gibbons-Tsarev equation (GTe) to obtain some new results, including some Lie symmetries, one-parameter transformation groups, explicit invariant solutions in the form of power serie...
We reply to the comment by Frewer and Khujadze regarding our contribution “Lie Symmetry Analysis of the Hopf Functional-Differential Equation” (Symmetry 2015, 7(3), 1536). The method developed by the present authors considered the Lie group analysis...
We perform Lie symmetry analysis to a zero-coupon bond pricing equation whose price evolution is described in terms of a partial differential equation (PDE). As a result, using the computer software package SYM, run in conjunction with Mathematica, a...
In this paper, we study a viscous Cahn–Hilliard equation from the point of view of Lie symmetries in partial differential equations. The analysis of this equation is motivated by its applications since it serves as a model for many problems in...
In this paper, we scrutinize a generalized (2+1)-dimensional nonlinear wave equation (NWE) which describes the waves propagation in plasma physics by utilizing Lie group analysis, Lie point symmetry are obtained and thereafter symmetry reductions are...
This review begins with the standard Lie symmetry theory for nonlinear PDEs and explores extensions of symmetry analysis. First, it introduces three key symmetry reduction methods: the classical symmetry method, conditional symmetries, and the CK dir...
There are many routines developed for solving ordinary differential Equations (ODEs) of different types. In the case of an nth-order ODE that admits an r-parameter Lie group (3≤r≤n), there is a powerful method of Lie symmetry analysis by which...
Lie symmetry analysis of differential equations provides a powerful and fundamental framework to the exploitation of systematic procedures leading to the integration by quadrature (or at least to lowering the order) of ordinary differential equations...
The basic idea of the ‘partially nonclassical method’, developed in the present paper, is to apply the invariance requirement of the Lie group method using not all differential consequences of the invariant surface condition but only part...
In this work, we investigate invariance analysis, conservation laws, and exact power series solutions of time fractional generalized Drinfeld–Sokolov systems (GDSS) using Lie group analysis. Using Lie point symmetries and the Erdelyi–Kober (EK) fract...
Group classification is a powerful tool for identifying and selecting the free elements—functions or parameters—in partial differential equations (PDEs) that maximize the symmetry properties of the model. In this paper, we revisit the gro...
This work investigates the stability analysis of linear control systems defined on Lie groups, with a particular focus on low-dimensional cases. Unlike their Euclidean counterparts, such systems evolve on manifolds with non-Euclidean geometry, where...
This review article explores the theory of control sets for linear control systems defined on two-dimensional Lie groups, with a focus on the plane R2 and the affine group Aff+(2). We systematically summarize recent advances, emphasizing how the geom...
In this paper, we study the Camassa–Holm type equation, which has applications in mathematical physics and engineering. Its applications extend across disciplines, contributing to our understanding of complex systems and helping to develop inno...
Some recent results on approximate Lie group methods and previously developed concepts on potential symmetries are extended and applied to nonlinear systems perturbed to some order by a small parameter. The potential (or auxiliary) form of the pertur...
This work investigates a class of susceptible–infected–susceptible (SIS) epidemic model with reaction–diffusion–advection (RDA) by utilizing the Lie group methods. The Lie symmetries are computed for the three widely used inci...
Heat transfer systems for chemical processes must be designed to be as efficient as possible. As heat transfer is such an energy-intensive stage in many chemical processes, failing to focus on efficiency can push up costs unnecessarily. Many problems...
The analysis of the present paper reveals that, besides the relativistic symmetry expressed by the Lorentz group of coordinate transformations which leave invariant the Minkowski metric of space-time of inertial frames, there exists one more relativi...
The study of non-linear partial differential equations is a complex task requiring sophisticated methods and techniques. In this context, we propose a neural network approach based on Lie series in Lie groups of differential equations (symmetry) for...
Many physical phenomena in fields of studies such as optical fibre, solid-state physics, quantum field theory and so on are represented using nonlinear evolution equations with variable coefficients due to the fact that the majority of nonlinear cond...
The current study presents a comprehensive Lie symmetry analysis for the time-fractional Mikhailov–Novikov–Wang (MNW) system with the Riemann–Liouville fractional derivative. The corresponding simplified equations with the Erd&eacut...
The invariance method, known as Lie analysis, consists of finding a group of transformations that leave a difference equation invariant. This powerful tool permits one to lower the order, linearize and more importantly, obtain analytical solutions of...
The group classification of a class of time fractional generalized KdV equations with variable coefficient is presented. The Lie symmetry analysis method is extended to the certain subclasses of time fractional generalized KdV equations with initial...
Basener and Ross (2005) proposed a mathematical model that describes the dynamics of growth and sudden decrease in the population of Easter Island. We have applied Lie group analysis to this system and found that it can be integrated by quadrature if...
This paper tackles the ill-posed inversion of initial conditions and diffusion coefficient for Burgers’ equation with a source term. Using optimal control theory combined with a finite difference discretization scheme and a dual-functional desc...
In this research paper, we study symmetry groups, soliton solutions, and the dynamical behavior of the Ivancevic Option Pricing Model (IOPM). First, we find the Lie symmetries of the considered model; next, we use them to determine the corresponding...
The nonlinear phenomena in numbers are modelled in a wide range of fields such as chemical physics, ocean physics, optical fibres, plasma physics, fluid dynamics, solid-state physics, biological physics and marine engineering. This research article s...
In contrast to diradicals connected by alternant hydrocarbons, only a few studies have addressed diradicals connected by nonalternant hydrocarbons and their heteroatom derivatives. Here, the synthesis, structure, and magnetic properties of pyrrole-2,...
This analysis is interested in the dynamic flow of incompressible triple diffusive fluid flowing through a linear stretched surface. The current study simulates when Boussinesq approximation and MHD are significant. As for originality, a comparative...
Group theoretic analysis is performed to get a new Lie group of transformations for non-linear differential systems constructed against mass and heat transfer in the thermally magnetized non-Newtonian fluid flow towards a heated stretched porous surf...
The paper studies an unsteady equation with quadratic nonlinearity in second derivatives, that occurs in electron magnetohydrodynamics. In mathematics, such PDEs are referred to as parabolic Monge–Ampère equations. An overview of the Mon...
This article deals with the presentation of an alternative approach that uses methods of geometric mechanics, which allow one to see into the geometrical structure of the equations and can be useful not only for modeling but also during the design of...
This study investigates the potential Kadomtsev–Petviashvili equation incorporating a power-type nonlinearity (PKPp), a model that features prominently in various nonlinear phenomena encountered in physics and applied mathematics. A complete No...
The Korteweg–de Vries (KdV) equation is a nonlinear evolution equation that reflects a wide variety of dispersive wave occurrences with limited amplitude. It has also been used to describe a range of major physical phenomena, such as shallow wa...
In this study, a new cobalt arsenate belonging to the alluaudite supergroup compounds with the general formula of Co3(AsO4)0.5+x(HAsO4)2−x(H2AsO4)0.5+x[(H,□)0.5(H2O,H3O)0.5]2x+ (denoted as CoAsAllu) was synthesized under hydrothermal cond...