zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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:
35Q53KdV-like (Korteweg-de Vries) equations
35C07Traveling wave solutions of PDE
35A30Geometric 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=μuxx, 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