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Symbolic computation of solutions for a forced Burgers equation. (English) Zbl 1185.35238
Summary: We give exact solutions for a forced Burgers equation. We make use of the generalized Cole-Hopf transformation and the traveling wave method.
##### MSC:
 35Q53 KdV-like (Korteweg-de Vries) equations 35C07 Traveling wave solutions of PDE 35A30 Geometric theory for PDE, characteristics, transformations
##### References:
 [1] Eule, S.; Friedrich, R.: A note on the forced Burgers equation, Physics letters A 351, 238-241 (2006) [2] Scott, M.: Encyclopedia of nonlinear science, (2005) [3] Bateman, H.: Some recent research on the motion of fluids, Monthly weather review 43, 163-170 (1915) [4] Burgers, J.: Application of a model system to illustrate some points of the statistical theory of free turbulence, Proceedings of the nederlandse akademie Van wetenschappen 43, 2-12 (1940) · Zbl 0061.45710 [5] Burgers, J.: A mathematical model illustrating the theory of turbulence, Advances in applied mechanics 1, 171-199 (1948) [6] Hopf, E.: The partial differential equation $ut+uux=\mu$uxx, Communications in pure and applied mathematics 3, 201-230 (1950) · Zbl 0039.10403 · doi:10.1002/cpa.3160030302 [7] Cole, J.: On a quasilinear parabolic equation occurring in aerodynamics, Quarterly journal of applied mathematics 9, 225-236 (1951) · Zbl 0043.09902 [8] Case, K. M.; Chiu, S. C.: Burgers turbulence models, Physics of fluids 12, 1799-1808 (1969) · Zbl 0193.27102 · doi:10.1063/1.1692744 [9] Burgers, J.: The nonlinear diffusion equation: asymptotic solutions and statistical problems, (1974) [10] Forsyth, A. R.: Theory of differential equations, (1906) [11] Calogero, F.; De Lillo, S.: The Burgers equation on the semiline, Inverse problems 5, L37 (1989) · Zbl 0778.35092 · doi:10.1088/0266-5611/5/4/001 [12] Olver, P.: Applications of Lie groups to differential equations, (1993) [13] Salas, A.: Some solutions for a type of generalized Sawada – Kotera equation, Applied mathematics and computation 196, 812-817 (2008) · Zbl 1132.35461 · doi:10.1016/j.amc.2007.07.013 [14] Salas, A. H.; Gómez, C. A.: Computing exact solutions for some fifth KdV equations with forcing term, Applied mathematics and computation 204, 257-260 (2008) · Zbl 1160.35526 · doi:10.1016/j.amc.2008.06.033 [15] Salas, A. H.: Exact solutions for the general fifth KdV equation by the exp function method, Applied mathematics and computation 205, 291-297 (2008) · Zbl 1160.35525 · doi:10.1016/j.amc.2008.07.013 [16] A.H. Salas, C.A. Gómez, Exact solutions for a third KdV equation with variable coefficients and forcing term, Mathematical Problems in Engineering, Hindawi, in press. · Zbl 1188.35168 · doi:10.1155/2009/737928