Internal solitary waves commonly observed in the coastal ocean are oftenmodeled by a nonlinear evolution equation of the Korteweg–de Vries type. Because these waves often propagate for long distances over several inertial periods, the effect of Earth’s background rotation is potentially significant. The relevant extension of the Kortweg–de Vries is then the Ostrovsky equation, which for interna...

We consider the nonlinear Klein-Gordon equation in R. We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the existence of such multi-solitary waves, provided the composing boosted standing waves are stable. It is obtained by solving the equation backward in time around a sequence of approximate multisolitary waves and showing co...

This paper presents a further numerical study of the interaction dynamics for solitary waves in a nonlinear Dirac field with scalar self-interaction by using a fourth order accurate Runge-Kutta discontinuous Galerkin method. Our experiments are conducted on the Dirac solitary waves with a phase difference. Some interesting phenomena are observed: (a) full repulsion in binary and ternary collisi...

It is shown that the regularized long-wave equation admits a family of solitary waves of depression. Some of these solitary waves are stable while others are unstable. The proof of stability and instability is based on the general theory of Grillakis, Shatah and Strauss. The results are illustrated by numerical simulation using a spectral discretization.

Long dynamo waves are a characteristic feature of interface dynamo models with spatially localized α and Ω effects. The evolution of such waves is described by the modified Korteweg–de Vries equation. Solutions to this equation take the form of solitary waves, breathers, and snoidal and cnoidal waves, and represent nonlinear waves of magnetic activity that migrate towards the equator, as observ...

We introduce the concept of this special focus issue on solitons in nonintegrable systems. A brief overview of some recent developments is provided, and the various contributions are described. The topics covered in this focus issue are the modulation of solitons, bores, and shocks, the dynamical evolution of solitary waves, and existence and stability of solitary waves and embedded solitons.

This paper concerns the orbital stability and instability of solitary waves of the system of coupling equations of Benjamin-Bona-Mahony type. By applying the abstract results of Grillakis, Shatah and Strauss and detailed spectral analysis, we obtain the existence and stability of the solitary waves.

The modelling of baroclinic tides generated in the northern South China Sea is studied using a fully-nonlinear non-hydrostatic numerical model. The focus of the modelling efforts was on the vertical structure of internal waves in the vicinity of the Luzon Strait. The barotropic tidal flow interacting with a two-ridge bottom topography in the area of the Luzon Strait produces a complex baroclini...

We find new analytic solitary-wave solutions of the higher order wave equations of Korteweg – De Vries (KdV) type (I), using the auxiliary function method. We study the dynamical properties of the solitary-waves by numerical simulations. It is shown that the solitary-waves are stable for wide ranges of the model coefficients. We study the dynamics of the two solitary-waves by using the analytic...