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Similarity solutions of the Burgers equation with linear damping

B. Mayil Vaganan, M. Senthil Kumaran
2004 Applied Mathematics Letters  
The Burgers equation with linear damping has been subjected to Lie's group theoretic method of infinitesimal transformation to derive its solutions.  ...  To the best of our knowledge, we are the first to obtain a new similarity variable for an equation of the Burgers type and therefore provide new solutions. (~)  ...  SIMILARITY SOLUTIONS The Burgers equation with linear damping is Ut -]-U~x ~-O'?Z ~ ltxx , (1) where cr > 0 is a constant.  ... 
doi:10.1016/j.aml.2003.06.013 fatcat:57eztohfkvdgrejtozp37a6n4q

Exactly Solvable Nonhomogeneous Burgers Equations with Variable Coefficients [article]

Sirin A. Buyukasik, Oktay K. Pashaev
2011 arXiv   pre-print
We consider a nonhomogeneous Burgers equation with time variable coefficients, and obtain an explicit solution of the general initial value problem in terms of solution to a corresponding linear ODE.  ...  As exactly solvable models, we study forced Burgers equations with constant damping and an exponentially decaying diffusion coefficient.  ...  Another important property of the Burgers equation is related with the rational type solutions.  ... 
arXiv:1104.4717v1 fatcat:wn3n5wdckjaxrddhexk6x7fluu

Madelung Representation and Exactly Solvable Schrodinger-Burgers Equations with Variable Parameters [article]

Sirin A. Buyukasik, Oktay K. Pashaev
2010 arXiv   pre-print
It allows us to find exact solutions of the nonlinear Madelung system in terms of solutions of the Schrodinger equation and the corresponding classical linear ODE with variable frequency and damping.  ...  For the complex velocity field the Madelung system takes the form of a nonlinear complex Schrodinger-Burgers equation, for which we obtain exact solutions using complex Cole-Hopf transformation.  ...  Then, the Madelung transform is a complex linearization transform, similar to the Cole-Hopf transformation, linearizing the nonlinear Burgers equation in terms of the linear heat equation, see [4] and  ... 
arXiv:1005.5059v1 fatcat:mcur6ye4drachdupedctb5urje

Exact solutions of forced Burgers equations with time variable coefficients

Şirin A. Büyükaşık, Oktay K. Pashaev
2013 Communications in nonlinear science & numerical simulation  
Indeed, the zeros of the heat equation solution lead to pole singularities for the Burgers solution.  ...  In this paper, we consider a forced Burgers equation with time variable coefficients of the form U t þ ð _ lðtÞ=lðtÞÞU þ UU x ¼ ð1=2lðtÞÞU xx À x 2 ðtÞx, and obtain an explicit solution of the general  ...  Indeed, analytic solutions of the Burgers equation can be obtained by the Cole-Hopf transformation, which transforms the nonlinear Burgers equation to a linear heat equation [4, 5] .  ... 
doi:10.1016/j.cnsns.2012.11.027 fatcat:4cfnzdyejfg5zhmi3nectqxmt4

Damping of large-amplitude solitary waves

Roger Grimshaw, Efim Pelinovsky, Tatiana Talipova
2003 Wave motion  
This work was carried out with partial support from INTAS (99-1068 and 01-2156) for EP, and INTAS (01-25) and RFBR (00-05-64223) for TT.  ...  In the Burgers model the back-face is described by the self-similar solution αu(x, t) = x t , (25) which is the same as when the viscosity is zero, but here in the extended Burgers model the self-similar  ...  νL << 1. (24) The adiabatic stage of the solitary wave damping in this case is quite similar to the adiabatic stage with the linear friction damping; the solitary wave keeps its form, and a very small  ... 
doi:10.1016/s0165-2125(02)00093-8 fatcat:zh4u2k7pxzeerkcmnlltw2hpfe

Solitons and diffusive modes in the noiseless Burgers equation: Stability analysis

Hans C. Fogedby
1998 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
The noiseless Burgers equation in one spatial dimension is analyzed from the point of view of a diffusive evolution equation in terms of nonlinear soliton modes and linear diffusive modes.  ...  The transient evolution of the profile is interpreted as a gas of right hand solitons connected by ramp solutions with superposed linear diffusive modes.  ...  GENERAL PROPERTIES The Burgers equation (1.1) has the form of a nonlinear diffusive evolution equation with a linear diffusive term controlled by the damping or viscosity ν and a nonlinear mode coupling  ... 
doi:10.1103/physreve.57.2331 fatcat:fpoa74ij7zezpd65xbpaedgivy

Solution and transcritical bifurcation of Burgers equation

Jia-Shi Tang, Ming-Hua Zhao, Feng Han, Liang Zhang
2011 Chinese Physics B  
We can obtain many exact solutions of the Burgers equation, discuss its transcritical bifurcation and control dynamical behaviours by extending the stable region.  ...  The transcritical bifurcation exists in the (2 + 1)-dimensional Burgers equation.  ...  [6] The result from the self-similar reduction of a generalized Burgers equation with nonlinear damping was obtained. [7] Burgers equation is a simple, but important physical equation.  ... 
doi:10.1088/1674-1056/20/2/020504 fatcat:gy3ntwnflffnbacoesv7gqr53y

Page 2007 of Mathematical Reviews Vol. , Issue 91D [page]

1991 Mathematical Reviews  
M. (1-AZ) Painlevé analysis of a coupled Burgers—heat-equation system, and nonclassical similarity solutions of the heat equation. Phys. D 41 (1990), no. 2, 208-218.  ...  Summary: “Painlevé analysis of a coupled Burgers—heat-equation system of partial differential equations, initially introduced in a study of nonclassical similarity solutions of the heat equation, re- veals  ... 

Page 7461 of Mathematical Reviews Vol. , Issue 96m [page]

1996 Mathematical Reviews  
The first relates the Burgers equation with a linear damping to the cylindrical Burgers equation while the second maps the KdV equation with a linear damping to the non- planar KdV equation.  ...  Summary: “The exact solutions of a compound KdV-Burgers equation are obtained by using a homogeneous balance method.  ... 

Solving Fractional Damped Burgers' Equation Approximately by Using The Sumudu Transform (ST) Method

2021 Baghdad Science Journal  
In this work, the fractional damped Burger's equation (FDBE) formula + − + = 0, ∈ℝ, > 0 , > 0 is solved by Sumudu transform (ST) method .  ...  The purpose of the method is based on the application of ST method to nonlinear fractional partial differential equations (NLFPDE). Same initial conditions( IC) are selected to clarify this method.  ...  Mohammad J. and Bashir A. (2013)(13) used laplace inversion technique method for solveing the fractional partial differential equations (FPDEs) In this study the fractional Damped Burgers' equation were  ... 
doi:10.21123/bsj.2021.18.1(suppl.).0803 fatcat:b6tsfyt7vrhfhanipzrdeyth4e

Alfvén-Magnetosonic Waves Interaction

K. Murawski
1992 Acta Physica Polonica. A  
The propagation of the magnetosonic waves is described by linearized Boussinesq-type equations with ponderomotive terms due to the Alfven wave. Both long and short Alfven waves are considered.  ...  Numerical results for the fast mode propagating perpendicular to the magnetic field show the effect of inhomogeneity and pumping on a shock as the solution of the homogeneous Burgers equation.  ...  Acknowledgements The author wishes to express his sincere thanks to the Solar Theory Group at St Andrews, especially Dr Bernard Roberts and Prof.  ... 
doi:10.12693/aphyspola.81.335 fatcat:gpdo3d7klrdeddvkystefcdhmi

Dynamical pinning and non-Hermitian mode transmutation in the Burgers equation

H.C. Fogedby
2001 European Physical Journal B : Condensed Matter Physics  
We discuss the mode spectrum in both the deterministic and noisy Burgers equations in one dimension.  ...  The soliton profile in the Burgers equation serves as a complex gauge field engendering a mode transmutation of diffusive modes into propagating modes and giving rise to a dynamical pinning of localized  ...  hand soliton for µ = −1 with p s = 2νu s , a solution of the growing (unstable) noiseless Burgers equation for ν → −ν.  ... 
doi:10.1007/pl00011097 fatcat:uy7uui657ve3hfe7nsgraa7oza

Page 3632 of Mathematical Reviews Vol. , Issue 97F [page]

1997 Mathematical Reviews  
These pulse solutions have a similar form to the pulse solitary wave solution of the KP equation, but with vary- ing parameters.  ...  971:35186 97f:35186 35Q53 Hai, Wen Hua (PRC-HUED-P; Changsha); Xiao, Yi (PRC-HUST-P; Wuhan) Soliton solutions of a Burgers-KdV equation with a small perturbation. (Chinese.  ... 

Computations of Nonlinear Propagation of Sound Emitted from High Speed Mixing Layers~!2009-10-22~!2010-02-25~!2010-05-04~!

J. Punekar, E. J. Avital, R. E. Musafir
2010 Open Acoustics Journal  
The mixing layers are of convective Mach numbers of 0.4, 0.8 and 1.2. The LES results agree qualitatively with known flow behavior.  ...  Non-linear sound propagation is investigated computationally by simulating compressible time-developing mixing layers using the Large Eddy Simulation (LES) approach and solving the viscous Burgers Equation  ...  ACKNOWLEDGEMENTS The support given by the UK Daphne Jackson trust is kindly acknowledged as well as the support given by the Royal Society under its international joint project scheme.  ... 
doi:10.2174/1874837601003010011 fatcat:agurv2ngzfbtjbttwoa2nvtlbe

Approximate Analytical Solution to Time-Fractional Damped Burger and Cahn-Allen Equations

A. Esen, N. M. Yagmurlu, O. Tasbozan
2013 Applied Mathematics & Information Sciences  
The aim of the present paper is to obtain the approximate analytical solutions of time-fractional damped burger and Cahn-Allen equations by means of the homotopy analysis method (HAM).  ...  In the HAM solution, there exists an auxiliary parameterh which provides a convenient way to adjust and check the convergence region of the solution series.  ...  the HAM solutions of time-fractional damped burger equation by Eq  ... 
doi:10.12785/amis/070533 fatcat:myxxcjy6l5gj5nd5jddq6rgbeq
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