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

Abstract

Whitham modulation theory for the two dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasi-linear 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 hyrdodynamic-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.

8 pages, 1 figure, one reference and final journal information added

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Cited by in corpus (5)

• Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type
• Whitham modulation theory for the defocusing nonlinear Schrodinger equation in two and three spatial dimensions
• Modulation theory for soliton resonance and Mach reflection
• Integrability, exact reductions and special solutions of the KP-Whitham equations
• Whitham modulation theory for the Zakharov-Kuznetsov equation and transverse instability of its periodic traveling wave solutions