18 research outputs found
Breather lattice and its stabilization for the modified Korteweg-de Vries equation
We obtain an exact solution for the breather lattice solution of the modified
Korteweg-de Vries (MKdV) equation. Numerical simulation of the breather lattice
demonstrates its instability due to the breather-breather interaction. However,
such multi-breather structures can be stabilized through the concurrent
application of ac driving and viscous damping terms.Comment: 6 pages, 3 figures, Phys. Rev. E (in press
Variational method for the nonlinear dynamics of an elliptic magnetic stagnation line
The nonlinear evolution
of the kink instability of a plasma
with an elliptic magnetic stagnation line is studied by means
of an amplitude expansion of the ideal magnetohydrodynamic equations.
Wahlberg et al. [12] have shown that, near marginal stability,
the nonlinear evolution of the stability can be described in terms
of a two-dimensional potential U(X,Y), where X and Y represent
the amplitudes of the perturbations with positive and negative
helical polarization. The potential U(X,Y) is found to be nonlinearly
stabilizing for all values of the polarization. In our paper a Lagrangian
and an invariant variational principle for two coupled nonlinear ordinal
differential equations describing the nonlinear evolution of the stagnation
line instability with arbitrary polarization are given. Using a trial function
in a rectangular box we find the functional integral. The general case for
the two box potential can be obtained on the basis of a different ansatz
where we approximate the Jost function by polynomials of order n instead
of a piecewise linear function. An example for the second order is
given to illustrate the general case. Some considerations concerning
solar filaments and filament bands (circular or straight) are
indicated as possible applications besides laboratory experiments
with cusp geometry corresponding to quadripolar cusp geometries for
some clouds and thunderstorms