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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.

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A new series of N,N'-dialkyl-N,N'-diacetate ethylenediamine, differing by the length of the carbon tails (8, 10, and 12), was synthesized in two steps. Their surface properties and aggregation behavior were studied in aqueous solution using pH titration, surface tension, zeta potential, dynamic light scattering (DLS), transmission electron microscopy (TEM), and fluorescence measurements. On the basis of the pKa values obtained, surface tension was measured, as well as key surface property parameters. Combined with the zeta potential and DLS results, the experiments produced vesicles and reflected their pH-controllability through subsequent TEM and fluorescence measurements. pH-switchability was found to be reversible by light transmittance. Emulsion stability of dodecane-in-water in different pH showed that emulsion type was reversed between "on" for the O/W emulsion type and "off" for the W/O.