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A Coupled System for Nonlinear Wave Propagation Combining Wake Field Generation with a Kerr-Nonlinearity

Three cases of nonlinear wave propagation in plasmas are studied, involving different wave modes. In all cases a generic system of equations is found, combining a Kerr-like self nonlinearity with nonlocal effects due to the generation of low-frequency wake fields. Using the conservation laws of the system, explicit expressions for the soliton acceleration and frequency conversion rate are found.