Geodesic
The Cauchy problem for a short-wave equation
Electronic journal of differential equations, Tome 2009 (2009)
We prove existence and uniqueness of solutions for the Cauchy problem of the simplest nonlinear short-wave equation, $u_{tx}=u-3u^{2}$, with periodic boundary condition.
Classification : 34A12, 34A34, 35Q35, 35Q53
Keywords: Cauchy problem, benjamin-bona-Mahony-perigrine equation, short-waves 
@article{EJDE_2009__2009__a111,
     author = {Gama,  Silvio Marques A. and Smirnov,  Gueorgui},
     title = {The {Cauchy} problem for a short-wave equation},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1171.35460},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a111/}
}
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%A Smirnov,  Gueorgui
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%J Electronic journal of differential equations
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%U http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a111/
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%F EJDE_2009__2009__a111
Gama,  Silvio Marques A.; Smirnov,  Gueorgui. The Cauchy problem for a short-wave equation. Electronic journal of differential equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a111/