We propose a simple general method for analytic determination of the boundaries of the expanding nonlinear oscillation zone occurring in the decay of a step problem for non-integrable dispersive wave equations. A remarkable feature of the method is that it essentially uses only the dispersionless limit and the linear dispersion relation of the original nonlinear dispersive wave system. A concrete example pertaining to collisionless plasma dynamics is considered and complete agreement with the results of earlier numerical simulations is demonstrated.
|Number of pages
|Physics Letters, Section A: General, Atomic and Solid State Physics
|Early online date
|8 Oct 2003
|Published - 24 Nov 2003