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Recently, Dyachenko & Zakharov (2011) have derived a compact form of the well known Zakharov integro-differential equation for the third order Hamiltonian dynamics of a potential flow of an incompress...
Abstract: We investigate the particle trajectories in an irrotational shallow water flow over a flat bed as periodic waves propagate on the water's free surface. Within the linear water wave theory, w...
Abstract: We investigate the particle trajectories in a constant vorticity shallow water flow over a flat bed as periodic waves propagate on the water's free surface. Within the framework of small amp...
Abstract: We present explicit solutions for the ordinary differential equations system describing the motion of the particles beneath small-amplitude capillary-gravity waves which propagate on the sur...
Abstract: Two-dimensional periodic surface waves propagating under the combined influence of gravity and surface tension on water of finite depth are considered. Within the framework of small-amplitud...
Abstract: We present a new kind of particle path in constant vorticity water of finite depth, within the framework of small-amplitude waves.
Abstract: We provide analytic solutions of the nonlinear differential equation system describing the particle paths below small-amplitude periodic gravity waves travelling on a constant vorticity curr...
We investigate the particle trajectories in a constant vorticity shallow water flow over a flat bed as periodic waves propagate on the water’s free surface. Within the framework of small amplitude wav...
We present explicit solutions for the ordinary differential equations system describing the motion of the particles beneath small-amplitude capillary-gravity waves which propagate on the surface of an...
Two-dimensional periodic surface waves propagating under the combined influence of gravity and surface tension on water of finite depth are considered. Within the framework of small-amplitude waves, w...
We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regim...
Numerous studies have identi ed large quantum mechanical e ects in the dynamics of liquid water. In this paper, we suggest that these e ects may have been overestimated due to the use of rigid water ...
Gas storage plays an essential role in both carbon sequestration and hydrogen-fuelled cars, two of the most touted green technologies. To date, however, most proposed methods for storing gases in thes...
The nonlinear dynamics of cnoidal waves, within the context of the general N-cnoidal wave solutions of the periodic Korteweg-de Vries (KdV) and Kadomtsev-Petvishvilli (KP) equations, are considered. T...
The complete mathematical and physical characterization of nonlinear water wave dynamics has been an important goal since the fundamental partial differential equations were discovered by Euler over 2...

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