This paper provides an investigation on nonlinear dynamic behaviors of the (3+1)-dimensional B-type Kadomtsev—Petviashvili equation, which is used to model propagation weakly dispersive waves in a fluid. With help Cole—Hopf transform, Hirota bilinear equation established, then symbolic computation with ansatz function schemes employed search for diverse exact solutions. Some new results such as...

In this paper we propose an accurate and fast numerical method to obtain scattering fields from lossy dispersive inhomogeneous planar layers for both TE and TM polarizations. A new method is introduced to analyze lossy Inhomogeneous Planar Layers. In this method by applying spline based Galerkin’s method of moment to scalar wave equation and imposing boundary conditions we obtain reflection and...

The weakor wave-turbulence problem consists of finding statistical states of a large number of interacting waves. These states are obtained by forcing and dissipating a conservative dispersive wave equation at disparate scales to model physical forcing and dissipation, and by predicting the spectrum, often as a Kolmogorov-like power law, at intermediate scales. The mechanism for energy transfer...

We prove stability for arbitrarily long times of the zero solution for the so-called β-plane equation, which describes the motion of a two-dimensional inviscid, ideal fluid under the influence of the Coriolis effect. The Coriolis force introduces a linear dispersive operator into the 2d incompressible Euler equations, thus making this problem amenable to an analysis from the point of view of no...

In this article, global-in-time dispersive estimates and Strichartz estimates are explored for the wave equation on three dimensional hyperbolic space. Due to the negative curvature, extra dispersion is noted, as compared to the Euclidean case, and a wider range of Strichartz estimates are proved. Using these, small data global existence to semilinear wave equations is shown for a range of powe...

We analyze and implement fully discrete schemes for periodic initial value problems for a general class of dispersively modified Kuramoto–Sivashinsky equations. Time discretizations are constructed using linearly implicit schemes and spectral methods are used for the spatial discretization. The general case analyzed covers several physical applications arising in multi-phase hydrodynamics and t...

We study the dispersive character for waves on the one-dimensional free surface of an infinitely deep perfect fluid under the influence of surface tension. The main result state that, on average in time, the solution of the water-wave problem gains locally 1/4 derivative of smoothness in the spatial variable, compared to the initial state. The regularizing effect is a direct consequence of disp...

Considered in this report is the one-dimensional fourth-order dispersive cubic nonlinear Schrödinger equation with mixed dispersion. Orbital stability, in the energy space, of a particular standing-wave solution is proved in the context of Hamiltonian systems. The main result is established by constructing a suitable Lyapunov function.