We consider the stability of ground state solitary waves of the generalized Ostrovsky equation (ut − βuxxx + f(u)x)x = γu, with homogeneous nonlinearities of the form f(u) = ae|u| + ao|u|u. We obtain bounds on the function d whose convexity determines the stability of the solitary waves. These bounds imply that, when 2 ≤ p < 5 and ao < 0, solitary waves are stable for c near c∗ = 2 √ βγ. These ...

Laboratory experiments and field observations suggest that the degeneration of basin-scale internal standing waves into packets of solitary waves is an important mechanism for the transfer of energy within the internal wavefield in lakes. Since these shorter solitary waves break at the boundaries, this process provides a flux path from the wind to the turbulent benthic boundary layer. However, ...

We study the solitary waves and their interaction for a six-order generalized Boussinesq equation (SGBE) both numerically and analytically. A shooting method with appropriate initial conditions, based on the phase plane analysis around the equilibrium point, is used to construct the solitary-wave solutions for this nonintegrable equation. A symmetric three-level implicit finite difference schem...

We propose consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previous...

The amplitude of solitary waves significantly affects the properties of the waves by changing their degree of nonlinearity. The period of solitary waves e.g. decreases nonlinearly with amplitude. Observations of solitary waves propagating under similar stratification conditions, but with different amplitudes, were compared to identify how the wave period depends on wave amplitude under field co...

We predict the existence of gray (dark) solitary waves in negative-index materials on the basis of a derived higher-order nonlinear Schrödinger equation. The conditions for the formation of three cases of gray solitary waves and exact analytical expressions are presented. Furthermore, we investigate the properties of these gray solitary waves in negative-index materials. The results show that t...

In the long-wave, weakly nonlinear limit a generic model for the interaction of two waves with nearly coincident linear phase speeds is a pair of coupled Korteweg-de Vries equations. Here we consider the simplest case when the coupling occurs only through linear non-dispersive terms, and for this case delineate the various families of solitary waves that can be expected. Generically, we demonst...

The objective of this study was to investigate experimentally solitary waves run-up on sloping beaches. Conducted in the Super wave flume(5m×5.2m×300m) and the Large wave flume(2m×2m×200m)at Tainan Hydraulics Laboratory (THL), solitary waves were generated by moving the wave board forward in the manner of ramp-trajectory and solitary-wave-trajectory separately to simulate the various of wave he...

We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding solitary waves. The first order equation is shown to be equivalent to the Korteweg−de Vries (KdV) equation, while the second order equation is solved numeric...

Solitary waves with large electric fields (up to 100’s of mV/m) have been observed throughout the magnetosphere and in the bow shock. We discuss observations by Polar at high altitudes (∼ 4–8RE), during crossings of the plasma sheet boundary and cusp, and new measurements by Polar at the equatorial magnetopause and by Cluster near the bow shock, in the cusp and at the plasma sheet boundary. We ...