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

Gino Biondini, Mark A. Hoefer, Antonio Moro

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

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 systems into two parts: (i) a decoupled, independent two-component system comprised of the dispersionless KP equation, (ii) an auxiliary, two-component system coupled to the mean flow equations, which describes either the evolution of a linear wave or a soliton propagating on top of the mean flow. The integrability of both four-component systems is then demonstrated by applying the Haantjes tensor test as well as the method of hydrodynamic reductions. Various exact reductions of these systems are then presented that correspond to concrete physical scenarios.

Original languageEnglish
Pages (from-to)4114-4132
Number of pages19
JournalNonlinearity
Volume33
Issue number8
Early online date3 Jul 2020
DOIs
Publication statusPublished - 1 Aug 2020

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