Generalized Solutions to Fifth-Order Evolution Equations
نویسندگان
چکیده
منابع مشابه
Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations.
Solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations, such as the Korteweg-de Vries (KdV), nonlinear Schrödinger, and the Kadomtsev-Petviashvili equations. These integrable equations have linear dispersion and the solitons have infinite support. We have derived and investigate a new KdV-like Hamiltonian partial diffe...
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The Kawahara and modified Kawahara equations are fifth-order KdV type equations and have been derived to model many physical phenomena such as gravitycapillary waves and magneto-sound propagation in plasmas. This paper establishes the local well-posedness of the initial-value problem for Kawahara equation in H(R) with s > − 4 and the local well-posedness for the modified Kawahara equation in H(...
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We consider fifth-order nonlinear dispersive K(m,n, p) type equations to study the effect of nonlinear dispersion. Using simple scaling arguments we show, how, instead of the conventional solitary waves like solitons, the interaction of the nonlinear dispersion with nonlinear convection generates compactons the compact solitary waves free of exponential tails. This interaction also generates ma...
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Solutions of a class of fth-order model evolution equations corresponding to initial data in relatively weak function spaces are shown to exhibit a smoothing eeect of the type of Kato. These models include the next hierarchy of the Korteweg-de Vries equation. It is interesting to observe that conditions that guarantee smoother solutions in some of these weaker function spaces are exactly the on...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2001
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.7368