Integrability, exact reductions and special solutions of the KP–Whitham equations

@article{Biondini2020IntegrabilityER,
  title={Integrability, exact reductions and special solutions of the KP–Whitham equations},
  author={Gino Biondini and Mark A. Hoefer and Antonio Moro},
  journal={Nonlinearity},
  year={2020},
  volume={33},
  pages={4114 - 4132}
}
Reductions of the KP–Whitham system, namely the (2+1)-dimensional hydrodynamic system of five equations that describes the slow modulations of periodic solutions of the Kadomtsev–Petviashvili (KP) equation, are studied. Specifically, the soliton and harmonic wave limits of the KP–Whitham system are considered, which give rise in each case to a four-component (2+1)-dimensional hydrodynamic system. It is shown that a suitable change of dependent variables splits the resulting four-component… 
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