One parameter family of Compacton Solutions in a class of Generalized Korteweg-DeVries Equations
نویسندگان
چکیده
We study the generalized Korteweg-DeVries equations derivable from the Lagrangian: L(l, p) = ∫ ( 1 2φxφt − (φx) l(l−1) + α(φx) (φxx) 2 ) dx, where the usual fields u(x, t) of the generalized KdV equation are defined by u(x, t) = φx(x, t). For p an arbitrary continuous parameter 0 < p ≤ 2, l = p + 2 we find compacton solutions to these equations which have the feature that their width is independent of the amplitude. This generalizes previous results which considered p = 1, 2. For the exact compactons we find a relation between the energy, mass and velocity of the solitons. We show that this relationship can also be obtained using a variational method based on the principle of least action. PACS numbers: 03.40.Kf, 47.20.Ky, Nb, 52.35.Sb
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