Whitham modulation theory for the two-dimensional Benjamin-Ono equation.
basic_science · Level V
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- Record sourced from PubMed, PMID 29346943.
- Also identified by DOI 10.1103/PhysRevE.96.032225.
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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.