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Large amplitude internal waves are commonly observed in the coastal ocean. In the weakly nonlinear long wave régime, they are often modeled by the Korteweg-de Vries equation, which predicts that the long-time outcome of generic localised initial conditions is a train of internal solitary waves. However, when the effect of background rotation is taken into account, it is known from several theor...

The global attraction is established for all finite energy solutions to a model U(1)-invariant nonlinear Klein-Gordon equation in one dimension coupled to a finite number of nonlinear oscillators: We prove that each finite energy solution converges as t → ±∞ to the set of all “nonlinear eigenfunctions” of the form φ(x)e−iωt if all oscillators are strictly nonlinear, and the distances between al...

We investigate envelope solitary waves on square with two degrees of freedom and nonlinear nearest and next-nearest neighbor interactions. We consider solitary waves which are localized in the direction of their motion and periodically modulated along the perpendicular direction. In the quasi{monochromatic approximation and low{amplitude limit a system of two coupled nonlinear Schrr odinger equ...

In nonlinear science, it is very difficult to find exact interaction solutions among solitons and other kinds of complicated waves such as cnoidal waves and Painlevé waves. Actually, even if for the most well-known prototypical models such as the Kortewet-de Vries (KdV) equation and the Kadomtsev-Petviashvili (KP) equation, this kind of problem has not yet been solved. In this paper, the explic...

[1] The generation of secondary internal waves by the interaction of a large-amplitude internal solitary wave with the Dreadnought Bank in the Andaman Sea (6 400N, 95 470E) is shown by analyzing a synthetic aperture radar (SAR) image acquired by the European Remote Sensing satellite ERS-2 and by carrying out model calculations. Although the Dreadnought Bank is quite deep (241 m), the model calc...

The problem of modulation instability of a self-focused beam in a homogeneous nonlinear medium with saturation and anomalous group-velocity dispersion is solved numerically. It is shown that the results of this instability is beam breakup into a periodic train of three-dimensional (3D) spatial solitary waves. It is also shown that other types of periodic initial conditions can produce a periodi...

We investigate envelope solitary waves on square with two degrees of freedom and nonlinear nearest and next-nearest neighbor interactions. We consider solitary waves which are localized in the direction of their motion and periodically modulated along the perpendicular direction. In the quasi– monochromatic approximation and low–amplitude limit a system of two coupled nonlinear Schrödinger equa...

The objective of this paper is to study the existence of solitary wave solutions of a fifth order model equation for steady capillary-gravity waves over a bump with the Bond number near 1/3. We proved that there exist solitary wave solutions of the model equation for a sufficiently smooth compact bump. Key-Words: Steady capillary-gravity wave, Solitary wave solution, Compact bump.

Note that 40 determines the initial position of the wave, and that, due to the square root in (1.2), the parameter P can only take values in 0<P=< 1. Thus, the solitary waves (1.1) only exist for a finite range of velocities l < c < l . Of course, a positive (respectively negative) velocity corresponds to a wave moving to the right (respectively to the left). When two solitary waves with parame...