# 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…

## 3 Citations

Oblique interactions between solitons and mean flows in the Kadomtsev–Petviashvili equation

- Physics
- 2020

The interaction of an oblique line soliton with a one-dimensional dynamic mean flow is analyzed using the Kadomtsev–Petviashvili II (KPII) equation. Building upon previous studies that examined the…

Modulation theory for soliton resonance and Mach reflection

- Physics, MathematicsProceedings of the Royal Society A
- 2022

Resonant Y-shaped soliton solutions to the Kadomtsev–Petviashvili II (KPII) equation are modelled as shock solutions to an infinite family of modulation conservation laws. The fully two-dimensional…

Evolution of truncated and bent gravity wave solitons: the Mach expansion problem

- PhysicsJournal of Fluid Mechanics
- 2020

Abstract The dynamics of initially truncated and bent line solitons for the Kadomtsev–Petviashvili (KPII) equation modelling internal and surface gravity waves is analysed using modulation theory. In…

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