In this work G'/G-expansion method has been employed to solve (2+1)-dimensional dispersive long wave equation. It is shown that G'/G-expansion method, with the help of symbolic computation, provides a very effective and powerful mathematical tool, for solving this equation.

The shallow water magnetohydrodynamic system describes the thin layer evolution of the solar tachocline. It is obtained from the three dimensional incompressible magnetohydrodynamic system similarly as the classical shallow water system is obtained from the incompressible NavierStokes equations. The system is hyperbolic and has two additional waves with respect to the shallow water system, the ...

The transformation of a weakly nonlinear interfacial solitary wave in an ideal twolayer flow over a step is studied. In the vicinity of the step the wave transformation is described in the framework of the linear theory of long interfacial waves, and the coefficients of wave reflection and transmission are calculated. A strong transformation arises for propagation into shallower water, but a we...

In this study, the (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation that indicated propagation of nonlinear dispersive waves in inhomogeneous media is given for consideration. The generalized exponential rational function method used to seek some new exact solutions considered equation. three-dimensional surfaces and two-dimensional graphs obtained are plotted by choosing appropriate values...

This paper presents an efficient numerical algorithm for the nonlinear wave-wave interactions that can be important in the evolution of coastal waves. Random sea waves of multiple frequencies always interact with each other and with the variable wind and pressure fields. As waves propagate and transform from deep to shallow water, it is generally difficult to determine the actual amount of nonl...

The long term goals are to (1) understand the role of wave-induced bubbles in the upper ocean boundary layer on the performance of underwater communications systems and ambient noise generation, (2) study the implications of focusing by surface gravity waves on Doppler sonar and acoustic communications systems in shallow and very shallow water, and (3) study the performance of acoustic vector s...

In the propagation and evolution of sea waves, previous studies pointed out that occurrence freak wave height is significantly related to quasi-resonant four-wave interaction in modulated waves. From numerical--experimental study over an uneven bottom, nonlinear effect caused by bathymetry change also contributes extreme events unidirectional To comprehensively analyse two-dimensional wavefield...

The Ostrovsky–Hunter equation governs evolution of shallow water waves on a rotating fluid in the limit of small high-frequency dispersion. Sufficient conditions for the wave breaking in the Ostrovsky–Hunter equation are found both on an infinite line and in a periodic domain. Using the method of characteristics, we also specify the blow-up rate at which the waves break. Numerical illustrations...

We study the maximum wave amplitude produced by line-soliton interactions of the Kadomtsev-Petviashvili II (KPII) equation, and we discuss a mechanism of generation of large amplitude shallow water waves by multi-soliton interactions of KPII. We also describe a method to predict the possible maximum wave amplitude from asymptotic data. Finally, we report on numerical simulations of multi-solito...