Symbolic computation of solutions for a forced Burgers equation

In this paper we give exact solutions for a forced Burgers equation. We make use of the generalized Cole-Hopf transformation and the traveling wave method.

[1]  J. Burgers Hydrodynamics. — Application of a model system to illustrate some points of the statistical theory of free turbulence , 1995 .

[2]  S CesarA.Gómez,et al.  Exact Solutions for a Third-Order KdV Equation with Variable Coefficients and Forcing Term , 2009 .

[3]  A. Jamiołkowski Book reviewApplications of Lie groups to differential equations : Peter J. Olver (School of Mathematics, University of Minnesota, Minneapolis, U.S.A): Graduate Texts in Mathematics, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1986, XXVI+497pp. , 1989 .

[4]  A. R. Forsyth Theory of Differential Equations , 1961 .

[5]  E. Hopf The partial differential equation ut + uux = μxx , 1950 .

[6]  A. Scott Encyclopedia of nonlinear science , 2006 .

[7]  Alvaro H. Salas,et al.  Exact solutions for the general fifth KdV equation by the exp function method , 2008, Appl. Math. Comput..

[8]  Cesar Augusto Gómez Sierra,et al.  Computing exact solutions for some fifth KdV equations with forcing term , 2008, Appl. Math. Comput..

[9]  Alvaro Salas,et al.  Some solutions for a type of generalized Sawada-Kotera equation , 2008, Appl. Math. Comput..

[10]  K. Case,et al.  Burgers' Turbulence Models , 1969 .

[11]  J. Burgers A mathematical model illustrating the theory of turbulence , 1948 .

[12]  Johannes Martinus Burgers,et al.  The Nonlinear Diffusion Equation: Asymptotic Solutions and Statistical Problems , 1974 .

[13]  F. Calogero,et al.  Burgers equation on the semiline , 1989 .

[14]  H. Bateman,et al.  SOME RECENT RESEARCHES ON THE MOTION OF FLUIDS , 1915 .

[15]  R. Friedrich,et al.  A note on the forced Burgers equation , 2005, nlin/0509006.

[16]  J. Cole On a quasi-linear parabolic equation occurring in aerodynamics , 1951 .