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Similarity solutions of the Burgers equation with linear damping

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. ...

##
###
Exactly Solvable Nonhomogeneous Burgers Equations with Variable Coefficients
[article]

2011
*
arXiv
*
pre-print

We consider a nonhomogeneous

arXiv:1104.4717v1
fatcat:wn3n5wdckjaxrddhexk6x7fluu
*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*. ...##
###
Madelung Representation and Exactly Solvable Schrodinger-Burgers Equations with Variable Parameters
[article]

2010
*
arXiv
*
pre-print

It allows us to find exact

arXiv:1005.5059v1
fatcat:mcur6ye4drachdupedctb5urje
*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 ...##
###
Exact solutions of forced Burgers equations with time variable coefficients

2013
*
Communications in nonlinear science & numerical simulation
*

Indeed,

doi:10.1016/j.cnsns.2012.11.027
fatcat:4cfnzdyejfg5zhmi3nectqxmt4
*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] . ...##
###
Damping of large-amplitude solitary waves

2003
*
Wave motion
*

This work was carried out

doi:10.1016/s0165-2125(02)00093-8
fatcat:zh4u2k7pxzeerkcmnlltw2hpfe
*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 ...##
###
Solitons and diffusive modes in the noiseless Burgers equation: Stability analysis

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 ...

##
###
Solution and transcritical bifurcation of Burgers equation

2011
*
Chinese Physics B
*

We can obtain many exact

doi:10.1088/1674-1056/20/2/020504
fatcat:gy3ntwnflffnbacoesv7gqr53y
*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*. ...##
###
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,

doi:10.21123/bsj.2021.18.1(suppl.).0803
fatcat:b6tsfyt7vrhfhanipzrdeyth4e
*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 ...##
###
Alfvén-Magnetosonic Waves Interaction

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. ...

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

2001
*
European Physical Journal B : Condensed Matter Physics
*

We discuss

doi:10.1007/pl00011097
fatcat:uy7uui657ve3hfe7nsgraa7oza
*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. ...##
###
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~!

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. ...

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

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 ...

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