Wave interactions in the singular Zakharov system

A multiscale perturbation method is used to derive solutions to the singular Zakharov equations governing the interaction of an acoustic wave with a plasma envelope. The method is described in general terms and then used to study two specific interactions. The first is that of a plasma standing wave with a monochromatic acoustic plane wave, the second is that of plasma soliton with a monochromatic plane wave. Systems of modulation equations governing the leading‐order interactions and higher‐order interactions are derived and solved. The higher‐order interaction equations ultimately reduce to solving a Schrodinger eigenvalue problem that can be solved using hypergeometric functions. The solutions are examined for fixed time as e is increased and for fixed e as time evolves.

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