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- W2320006575 abstract "Abstract In this paper, the semi-inverse method and the integral bifurcation method were used to study a generalized KdV equation, two kinds of new periodic loop solitons were obtained for the first time, their dynamic characters were investigated. Keywords: Generalized KdV equation; Integral bifurcation method; Semi-inverse method; Periodic loop solitons with local energy loss. 1 Introduction In this paper we consider the following nonlinear generalized KdV equation: uu u u uu t x xxt xxx x ++ + +ν βα 1(2)3 xxx x xx ++αν uu u u =0, (1) where α,,βν are real parameters. This equation was first proposed by Fokas [1] from physical considerations via a methodology which was introduced by Fuchssteiner and Fokas [2]. Eq.(1) can also be derived by the approach described in [3] and also be derived from the equation 1 qq tx ()θθ21+= − 0 where 3312 1,( x xxx3 x θνθ βα=∂ + ∂ =∂ + ∂ + ∂ q +∂ x q ) and (), 31 . uq x νν xxquxx =∂+∂ = + − u x Unlike KdV equation, Eq. (1) has very strong nonlinear structure. Thus, this equation exhibits a much richer phenomenology than KdV equation. In particular, it possesses compactons [4] (if" @default.
- W2320006575 created "2016-06-24" @default.
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- W2320006575 date "2008-01-01" @default.
- W2320006575 modified "2023-10-16" @default.
- W2320006575 title "New Periodic Loop Solitons of the Generalized KdV Equation" @default.
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- W2320006575 doi "https://doi.org/10.1515/ijnsns.2008.9.4.441" @default.
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