Growth rates of bending KdV solitons

Nonlinear ion-acoustic waves in magnetized plasmas are investigated. In strong magnetic fields they can be described by a Korteweg-de Vries (KdV) type equation. It is shown that these plane soliton solutions become unstable with respect to bending distortions. Variational principles are derived for the maximum growth rate #betta# as a function of the transverse wave number k of the perturbations. The results show that the growth rate peaks at a certain value of k and a cut-off ksub(c) exists. In the region where the #betta#(k) curve was not predicted numerically with high accuracy, i.e. near the cut-off, are found very precise analytical estimates. These findings are compared with previous results. For k >= ksub(c), stability with respect to transverse perturbations is proved. (author)