The harmonic and soliton limits of the KP-Whitham system decouple into the dispersionless KP equation plus auxiliary wave or soliton equations, and both four-component systems are integrable.
Whitham modulat ion theory for the Kadomtsev- Petviashvili equation
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Integrability, exact reductions and special solutions of the KP-Whitham equations
The harmonic and soliton limits of the KP-Whitham system decouple into the dispersionless KP equation plus auxiliary wave or soliton equations, and both four-component systems are integrable.