228 Results Found

The dynamic behavior variation of the Benjamin–Bona–Mahony–Burger (BBM-Burger) equation has been investigated in this paper. The modified auxiliary equation method (MAEM) and Ricatti–Bernoulli (RB) sub-ODE method, two of the m...

We consider fractional-in-space analogues of Burgers equation and Korteweg-de Vries-Burgers equation on bounded domains. Namely, we establish sufficient conditions for finite-time blow-up of solutions to the mentioned equations. The obtained conditio...

We provide a lower bound for the blow up time of the $H^2$ norm of the entropy solutions of the inviscid Burgers equation in terms of the $H^2$ norm of the initial datum. This shows an interesting symmetry of the Burgers equation: the invariance of the spa...

The coupled Burgers’ equation is a fundamental partial differential equation with applications in various scientific fields. Finding accurate solutions to this equation is crucial for understanding physical phenomena and mathematical models. Wh...

The new Laplace variational iterative method is used in this research for solving the (2+1)-D and (3+1)-D Burgers equations. This technique relies on the modified variational iteration method and the Laplace transform. To apply this approach, the dif...

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...

In this study, the evolution of surface water solitary waves under the action of Jeffreys’ wind–wave amplification mechanism in shallow water is analytically investigated. The analytic approach is essential for numerical investigations du...

In this study, the Lie group method for constructing exact and numerical solutions of the generalized time-dependent variable coefficients Burgers’, Burgers’–KdV, and KdV equations with initial and boundary conditions is presented. Lie group theory i...

This paper discusses the application of the orthogonal collocation on finite elements (OCFE) method using quadratic and cubic B-spline basis functions on partial differential equations. Collocation is performed at Gaussian points to obtain an optimal...

Burgers’ equation is used to describe wave phenomena in hydrodynamics and acoustics. It was derived originally as a prototype to provide analytic insight into the nature of turbulence and its modeling, and has found applications in the study of...

The Burgers’ equation is one of the nonlinear partial differential equations that has been studied by many researchers, especially, in terms of the fractional derivatives. In this article, the numerical algorithms are invented to obtain the app...

In this work, we consider some Burgers-like equations involving Laguerre derivatives and demonstrate that it is possible to construct specific exact solutions using separation of variables. We prove that a general scheme exists for constructing exact...

In this work we generate the numerical solutions of Burgers’ equation by applying the Crank-Nicholson method and different schemes for solving nonlinear systems, instead of using Hopf-Cole transformation to reduce Burgers’ equation into the linear he...

This investigation focuses on the study of the fractional damped Burgers’ equation by using the natural residual power series method coupled with the new iteration transform method in the context of the Caputo operator. The equation of Burgers...

It is well known that major error occur in the time integration instead of the spatial approximation. In this work, anisotropic kernels are used for temporal as well as spatial approximation to construct a numerical scheme for solving nonlinear Burge...

In this study, we sought numerical solutions for three-dimensional coupled Burgers’ equations. Burgers’ equations are fundamental partial differential equations in fluid mechanics. They integrate the characteristics of both the first-orde...

In the current work, the stochastic Burgers’ equation is studied using the Dynamically Orthogonal (DO) method. The DO presents a low-dimensional representation for the stochastic fields. Unlike many other methods, it has a time-dependent proper...

In the present work we introduced a new method and name it the conformable double Laplace decomposition method to solve one dimensional regular and singular conformable functional Burger’s equation. We studied the existence condition for the co...

In this Letter, the (G'/G) -expansion method is proposed to seek exact solutions of nonlinear evolution equations. For illustrative examples, we choose the compound KdV-Burgers equation, the compound KdV equation, the KdV-Burgers equation, the mKdV e...

In this paper, we discuss iterative and noniterative splitting methods, in theory and application, to solve stochastic Burgers’ equations in an inviscid form. We present the noniterative splitting methods, which are given as Lie–Trotter a...

This research paper introduces the generalized Burgers equation, a mathematical model defined using the general fractional derivative, the most recent operator in fractional calculus. The general fractional derivative can be reduced into three well-k...

The present work is concerned with the study of a generalized Langevin equation and its link to the physical theories of statistical mechanics and scale relativity. It is demonstrated that the form of the coefficients of the Langevin equation depends...

The newly constructed optimal perturbation iteration procedure with Laplace transform is applied to obtain the new approximate semi-analytical solutions of the fractional type of damped Burgers’ equation. The classical damped Burgers’ equ...

In this paper, three forms of (2 + l)-dimensional Burgers’ equations are investigated. More general multiple solutions of these Burgers’ equations are obtained by dependent variable transformation derived using the simplified homogeneous...

In this article, we have investigated the fractional-order Burgers equation via Natural decomposition method with nonsingular kernel derivatives. The two types of fractional derivatives are used in the article of Caputo–Fabrizio and Atangana–Baleanu...

In this paper, we construct an analytical solution of the coupled Burgers’ equation, using the homotopy analysis method, which is a semi-analytical method, the approximate solution obtained by this method is convergent for different values of t...

This article employs certain polynomials that generalize standard Fermat polynomials, called convolved Fermat polynomials, to numerically solve the fractional Burgers’ equation. New theoretical results of these polynomials are developed and uti...

In this paper, generalized symmetries and mCK method are employed to analyze the (2+1)-dimensional coupled Burgers equations. Firstly, based on the generalized symmetries method, the corresponding symmetries of the (2+1)-dimensional coupled Burgers e...

In this paper, we construct four numerical methods to solve the Burgers–Huxley equation with specified initial and boundary conditions. The four methods are two novel versions of nonstandard finite difference schemes (NSFD1 and NSFD2), explicit expon...

In this study, Gegenbauer wavelets are used to present two numerical methods for solving the coupled system of Burgers’ equations with a time-fractional derivative. In the presented methods, we combined the operational matrix of fractional inte...

In this article, two new modified variational iteration algorithms are investigated for the numerical solution of coupled Burgers’ equations. These modifications are made with the help of auxiliary parameters to speed up the convergence rate of...

In this paper, we develop a hybrid approach to solve the viscous Burgers’ equation by combining classical boundary layer theory with modern Physics-Informed Neural Networks (PINNs). The boundary layer theory provides an approximate analytical s...

In this work, nonlinear time-fractional coupled Burgers equations are solved utilizing a computational method, which is called the double and triple generalized-Laplace transform and decomposition method. We discuss the proof of triple generalized-La...

The second order Burger’s equation model is used to study the turbulent fluids, suspensions, shock waves, and the propagation of shallow water waves. In the present research, we investigate a numerical solution to the time fractional coupled-Bu...

This paper is related to the fractional view analysis of coupled Burgers equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of the Caputo-operator sense. In the current methodolo...

This paper explores an innovative expansion method for solving variable-coefficient partial differential equations. Combining specific auxiliary equations with the aid of mathematical software, our method achieves notable perspectives for understandi...

Most complex physical phenomena are described by non-linear Burgers’ equations, which help us understand them better. This article uses the transformation and the fractional Taylor’s formula to find approximate solutions for non-linear fr...

In this work, we obtain non-Gaussian (NG) stochastic solutions to $\chi$-Wick-type stochastic ($\chi$-Wk-TS) Burgers’ equations with variable coefficients. An Exp-function method, the connection between white noise theory and hypercomplex systems...

Burgers’ equation is a nonlinear partial differential equation that appears in various areas of physics and engineering. Finding accurate and efficient numerical methods to solve this equation is crucial for understanding complex fluid flow phe...

In this paper, we consider the time-fractional two-mode coupled Burgers equation with the Caputo fractional derivative. A modified homotopy perturbation method coupled with Laplace transform (He-Laplace method) is applied to find its approximate anal...

This research paper is about the new three wave, periodic wave and other analytical wave solutions of (2+1)-Dimensional Burgers equations by utilizing Hirota bilinear and extended sinh-Gordon equation expansion (EShGEE) schemes. Achieved solutions ar...

In this paper, we use the finite volume element method (FVEM) to approximate a one-dimensional, time fractional generalized Burgers’ equation. We construct the fully discrete finite volume element scheme for this equation by approximating the t...

In this paper, extended homogeneous balance method is presented with the aid of computer algebraic system Mathematica for deriving new exact traveling wave solutions for the foam drainage equation and the Kowerteg-de Vries–Burgers equation whic...

In this paper, we propose a 7th order weakly L-stable time integration scheme. In the process of derivation of the scheme, we use explicit backward Taylor’s polynomial approximation of sixth-order and Hermite interpolation polynomial approximat...

This research article introduces the four-dimensional natural transform Adomian decomposition method (FNADM) for solving the (3+1)-dimensional time-singular fractional coupled Burgers’ equation, along with its associated initial conditions. The...

In this paper, we propose the new iterative method (NIM) for solving the generalized Burgers–Huxley equation. NIM provides an approximate solution without the need for discretization and is based on a set of iterative equations. We compared the...

This article deals with a numerical approach based on the symmetric space-time Chebyshev spectral collocation method for solving different types of Burgers equations with Dirichlet boundary conditions. In this method, the variables of the equation ar...

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...

In this study, a relatively new method to solve partial differential equations (PDEs) called the fractional reduced differential transform method (FRDTM) is used. The implementation of the method is based on an iterative scheme in series form. We tes...

In this paper, to study the Sharma–Tasso–Olver–Burgers equation, we focus on the geometric properties and the exact traveling wave solutions. The corresponding traveling system is a cubic oscillator with damping, and it has time-dep...