Whitham modulation theory for the two-dimensional Benjamin-Ono equation

Mark Ablowitz, Gino Biondini, and Qiao Wang

Phys. Rev. E 96, 032225 – Published 25 September 2017

Abstract

Whitham modulation theory for the two-dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasilinear first-order partial differential equations is derived. The system describes modulations of the traveling wave solutions of the 2DBO equation. These equations are transformed to a singularity-free hydrodynamic-like system referred to here as the 2DBO-Whitham system. Exact reductions of this system are discussed, the formulation of initial value problems is considered, and the system is used to study the transverse stability of traveling wave solutions of the 2DBO equation.

Received 22 July 2017

DOI:https://doi.org/10.1103/PhysRevE.96.032225

Physics Subject Headings (PhySH)

Turbulence

Front propagation Nonlinear waves

Nonlinear DynamicsFluid Dynamics

Authors & Affiliations

Mark Ablowitz¹, Gino Biondini^2,3, and Qiao Wang²

¹Department of Applied Mathematics, State University of Colorado, Boulder, Colorado 80303, USA
²Department of Mathematics, State University of New York, Buffalo, New York 14260, USA
³Department of Physics, State University of New York, Buffalo, New York 14260, USA

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Issue

Vol. 96, Iss. 3 — September 2017

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