Geodesic
Exact solutions of a~generalized Boussinesq equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 23-34

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We analyze a generalized Boussinesq equation using the theory of symmetry reductions of partial differential equations. The Lie symmetry group analysis of this equation shows that the equation has only a two-parameter point symmetry group corresponding to traveling-wave solutions. To obtain exact solutions, we use two procedures: a direct method and the $G'/G$-expansion method. We express the traveling-wave solutions in terms of hyperbolic, trigonometric, and rational functions.
Keywords: partial differential equation, symmetry
Mots-clés : solution. 
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     author = {M. S. Bruz\'on},
     title = {Exact solutions of a~generalized {Boussinesq} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {23--34},
     publisher = {mathdoc},
     volume = {160},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a2/}
}
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M. S. Bruzón. Exact solutions of a~generalized Boussinesq equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 23-34. http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a2/