Abstract
Exact analytical solutions of a generic system of coupled ordinary differential equations for a pair of real scalar fields have been explicitly obtained. The equations may be considered to be the stationary form of the coupled time-dependent Schrodinger-Boussinesq (or Korteweg-de Vries) equations. The generic equations have six free parameters whereas it has been possible to obtain exact solutions valid on a five-dimensional hypersurface in six-dimensional parameter space using a technique developed by Varma and Rao (1980). While the solution for the variable of the Boussinesq (or Korteweg-de Vries) equation always has a symmetric structure, both symmetric and antisymmetric solutions are possible for the variable of the Schrodinger equation. The results are applied to an example dealing with the stationary propagation of coupled non-linear upper-hybrid and magnetosonic waves in magnetised plasmas.
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