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

References in corpus (3)

• On Dispersive and Classical Shock Waves in Bose-Einstein Condensates and Gas Dynamics
• Shocks in nonlocal media
• Whitham method for Benjamin-Ono-Burgers equation and dispersive shocks in internal waves in deep fluid