Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2003-04-04
Phys.Rev. E68 (2003) 016307
Nonlinear Sciences
Exactly Solvable and Integrable Systems
6 pages (RevTeX). Remarks added on transportation of energy from small initial scales to larger distances. To be published in
Scientific paper
10.1103/PhysRevE.68.016307
It is pointed out that for the case of (compressible) magnetohydrodynamics (MHD) with the fields $v_y(y,t)$ and $B_x(y,t)$ one can have equations of the Burgers type which are integrable. We discuss the solutions. It turns out that the propagation of the non-linear effects is governed by the initial velocity (as in Burgers case) as well as by the initial Alfv\'en velocity. Many results previously obtained for the Burgers equation can be transferred to the MHD case. We also discuss equipartition $v_y=\pm B_x$. It is shown that an initial localized small scale magnetic field will end up in fields moving to the left and the right, thus transporting energy from smaller to larger distances.
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