Stationary Solitons of the Fifth Order KdV-type Equations and their Stabilization

Details Stationary Solitons of the Fifth Order KdV-type Equations and their Stabilization Stationary Solitons of the Fifth Order KdV-type Equations and their Stabilization

1996-04-19

arxiv.org/abs/hep-th/9604122v1

Phys.Lett. A223 (1996) 449-452

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, no figures

Scientific paper

10.1016/S0375-9601(96)00772-4

Exact stationary soliton solutions of the fifth order KdV type equation $$ u_t +\alpha u^p u_x +\beta u_{3x}+\gamma u_{5x} = 0$$ are obtained for any p ($>0$) in case $\alpha\beta>0$, $D\beta>0$, $\beta\gamma<0$ (where D is the soliton velocity), and it is shown that these solutions are unstable with respect to small perturbations in case $p\geq 5$. Various properties of these solutions are discussed. In particular, it is shown that for any p, these solitons are lower and narrower than the corresponding $\gamma = 0$ solitons. Finally, for p = 2 we obtain an exact stationary soliton solution even when $D,\alpha,\beta,\gamma$ are all $>0$ and discuss its various properties.

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