Weakly nonlinear waves in elastic rods have been studied by many authors. Most studies concentrated on smooth solutions only. However, when waves are of moderate length, non-smooth waves, such as peakons (or solitary shock waves), can arise (see Dai and Huo 2000). For strongly nonlinear waves (not assuming the smallness of the wave amplitude), as far as the authors are aware, only incompressibl...

The objectives are to use a combination of theoretical and numerical models to study the evolution of the internal tide and its possible disintegration into internal solitary waves. A central aspect of this work is to explore the role of rotation in the process. Rotation permits the presence of periodic, nonlinear inertia-gravity waves (i.e., the tide) that can act as attractors and arrest the ...

Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a fully nonlinear thin shell model. Ful...

The interaction of interfacial solitary waves of algebraic type is investigated on the basis of a higherorder Benjamin-Ono equation. By developing a multisoliton perturbation theory, we show analytically that the overtaking collision between two solitary waves exhibits the phase shift but the amplitudes are not altered after interaction. The predication of the phase shift that takes place betwe...

Abstract. We prove the existence of a new type of solutions to a nonlinear Schrödinger system. These solutions, which we callmulti-speeds solitary waves, are behaving at large time as a couple of scalar solitary waves traveling at different speeds. The proof relies on the construction of approximations of the multi-speeds solitary waves by solving the system backwards in time and using energy m...

We present investigations into the collision of co-travelling solitary waves in a granular chain. Impulses are injected into the system by means of a piezo stack and the results are compared to a numerical model of discrete masses connected by non-linear springs. Similar to other solitary wave-carrying systems, a phase shift in both interacting solitary waves is observed due to their collision....

Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schrödinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, that span a large number of lattice periods. In this limit, the allowed positions of solitary waves relative to the lattice, as well as their linear stability properties, h...

We consider the existence and propagation of nondi ractive and nondispersive spatiotemporal optical wavepackets in nonlinear Kerr media. We report analytically and con rm numerically the properties of spatiotemporal dark line solitary wave solutions of the (2+1)D nonlinear Schrödinger equation (NLSE). Dark lines represent holes of light on a continuous wave background. Moreover, we consider non...

The rarefactive KdV solitary waves in a dusty plasma have been extensively studied analytically and found experimentally in the previous works. Though the envelope solitary wave described by a nonlinear Schrödinger equation (NLSE) has been proposed by using the reductive perturbation method, it is first verified by using the particle-in-cell (PIC) numerical method in this paper. Surprisingly, t...

Capillary gravity waves excited by an obstacle are investigated by numerical simulations. Under the resonant condition for which large-amplitude solitary waves are generated, solutions of the Euler equations show that the capillary effects induce the generation of short waves both upstream of the solitary waves and downstream of the obstacle. Overall characteristics of these waves agree with th...