Related papers: Hamiltonian approach to modelling interfacial inte…
A variable-coefficient forced Korteweg-de Vries equation with spacial inhomogeneity is investigated in this paper. Under constraints, this equation is transformed into its bilinear form, and multi-soliton solutions are derived. Effects of…
A localised overpressure translating at a uniform speed greater than a critical value acts at the interface between two deep fluid layers with different densities. We analyse the resulting wave patterns using an initial-value problem…
In this work we first study the quantum diffusion in a volume of a crystalline solid at high interstitial concentrations when the effects of the short-range interactions between the diffusing particles are to be factors. Within the scope of…
Internal tide generation and breaking play a primary role in the vertical transport and mixing of heat and other properties in the ocean interior, thereby influencing climate regulation. Additionally, internal tides increase sound speed…
We present a numerical study of essentially nonlinear dynamics of surface gravity waves on deep water with constant vorticity using governing equations in conformal coordinates. The dispersion relation of surface gravity waves on shear flow…
The dynamics of nonlinear waves with controllable dispersion, nonlinearities, and background continues to be an exciting line of research in recent years. In this work, we focus to investigate an integrable (3+1)-dimensional nonlinear model…
We compare dynamical and energetical stability criteria for vortex rings. It is argued that vortex rings will be intrinsically unstable against perturbations with short wavelengths below a critical wavelength, because the canonical vortex…
A wave equation, that governs finite amplitude acoustic disturbances in a thermoviscous Newtonian fluid, and includes nonlinear terms up to second order, is proposed. In contrast to the model known as the Kuznetsov equation, the proposed…
We investigate linear interference effects between a nonlinear plane wave and bright solitons, which are admitted by pair-transition coupled two-component Bose-Einstein condensate. We demonstrate the interference effects can induce several…
Direct numerical simulations of turbulent flow in a channel with one rigid and one viscoelastic wall are performed. An Eulerian-Eulerian model is adopted with a level-set approach to identify the fluid-compliant material interface. Focus is…
Processes of propagation and interaction of nonlinear gravity-capillary waves on the free surface of a deep non-conducting liquid with high dielectric constant under the action of a tangential electric field are numerically simulated. The…
We present a review of the normal form theory for weakly dispersive nonlinear wave equations where the leading order phenomena can be described by the KdV equation. This is an infinite dimensional extension of the well-known…
A model of nonlinear elastic medium with internal structure is considered. The medium is assumed to contain cavities, microcracks or blotches of substances that differ sharply in physical properties from the base material. To describe the…
General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and…
We investigate sound ray propagation in a range-dependent underwater acoustic waveguide. Our attention is focused on sensitivity of ray dynamics to the vertical structure of a sound-speed perturbation induced by ocean internal waves. Two…
A one-dimensional long-wave model of an unsteady three-layer flow of a stratified fluid under a lid is proposed, taking into account turbulent mixing in the intermediate layer. In the Boussinesq approximation, the equations of motion are…
The dynamics of the ultra-intense circularly polarized solitons under inhomogeneous plasmas are examined. The interaction is modeled by the Maxwell and relativistic hydrodynamic equations and is solved with fully implicit energy-conserving…
The inertial subrange of turbulence in a density stratified environment is the transition from internal waves to isotropic turbulence, but it is unclear how to interpret its extension to anisotropic stratified turbulence. Knowledge about…
Localized patterns and nonlinear oscillation formation on the bounded free surface of an ideal incompressible liquid are analytically investigated . Cnoidal modes, solitons and compactons, as traveling non-axially symmetric shapes are…
Recent developments of the weak turbulence theory applied to internal waves exhibit a power-law solution of the kinetic energy equation close to the oceanic Garrett \& Munk spectrum, confirming weakly nonlinear wave interactions as a likely…