Propagation of dust ion acoustic waves in plasmas composed of nonthermal distributed electrons and stationary dust particles is investigated. Nonlinear Schrdinger equation is derived to describe small amplitude waves, using the reduction perturbation technique. Modulation instability of dust ion acoustic waves is analysed for this system. Parametric investigation indicates that growth rate of...

The integrable 3rd-order Korteweg-de Vries (KdV) equation emerges uniquely at linear order in the asymptotic expansion for unidirectional shallow water waves. However, at quadratic order, this asymptotic expansion produces an entire family of shallow water wave equations that are asymptotically equivalent to each other, under a group of nonlinear, nonlocal, normal-form transformations introduce...

Numerical simulations of the recently derived fully nonlinear equations of motion for weakly threedimensional water waves [V.P. Ruban, Phys. Rev. E 71, 055303(R) (2005)] with quasi-random initial conditions are reported, which show the spontaneous formation of a single extreme wave on the deep water. This rogue wave behaves in an oscillating manner and exists for a relatively long time (many wa...

We study asymptotic stability of solitary wave solutions in the one-dimensional Benney-Luke equation, a formally valid approximation for describing two-way water wave propagation. For this equation, as for the full water wave problem, the classic variational method for proving orbital stability of solitary waves fails dramatically due to the fact that the second variation of the energy-momentum...

Numerical simulations of the recently derived fully nonlinear equations of motion for weakly threedimensional water waves [V.P. Ruban, Phys. Rev. E 71, 055303(R) (2005)] with quasi-random initial conditions are reported, which show the spontaneous formation of a single extreme wave on the deep water. This rogue wave behaves in an oscillating manner and exists for a relatively long time (many wa...

My long-term goal is to contribute, by means of an accurate hydrodynamics model, to efficient design, development and operation of autonomous underwater vehicles in energetic shallow waters. From a scientific viewpoint, the development of the AUV hydrodynamic model will contribute to a better understanding of wave-body-current interactions, nonlinear shallow-water waves, wave effects on stabili...

Ship maneuvering performance is typically predicted in calm water conditions. This provides very valuable information at the initial ship design stage. However, since the ship always sails in waves, the maneuvering performance of the ship in seaway may be significantly different from calm water condition. Therefore, if the effect of waves and the corresponding motion responses can be included i...

Roll waves are known to occur in the frictional flow of a thin layer of water down an inclined solid surface. For a layer of constant depth, the formation of these waves on a solid plane with small slope angle have been explained as a hydrodynamic instability occurring above a critical Froude number by analyzing the temporal stability of the constant velocity flow. Here we analyze the linear, s...

Stratified hydrostatic fluids have linear internal gravity waves with different phase speeds and vertical profiles. Here a simplified set of partial differential equations (PDE) is derived to represent the nonlinear dynamics of waves with different vertical profiles. The equations are derived by projecting the full nonlinear equations onto the vertical modes of two gravity waves, and the result...

geophysical fluids such as atmosphere and ocean often have stable density stratification; hence internal gravity waves are generated and propagated through them which are important in momentum and energy transfer in these media. these waves are also believed to generate layered structures in such media. recently there have been numerous theoretical, experimental and numerical studies on the way...