The strongly nonlinear long-wave model for large amplitude internal waves in a two-layer system is regularized to eliminate shear instability due to the wave-induced velocity jump across the interface. The model is written in terms of the horizontal velocities evaluated at the top and bottom boundaries instead of the depth-averaged velocities, and it is shown through local stability analysis th...

In this paper we study several aspects of solitary wave solutions of the Ostrovsky equation. Using variational methods, we show that as the rotation parameter goes to zero, ground state solitary waves of the Ostrovsky equation converge to solitary waves of the Korteweg-deVries equation. We also investigate the properties of the function d(c) which determines the stability of the ground states. ...

Since space charge waves on a particle beam exhibit both dispersive and nonlinear character, solitary waves or solitons are possible. Dispersive, nonlinear wave propagation in high current beams is found to be similar to ion-acoustic waves in plasmas with an analogy between Debye screening and beam pipe shielding. Exact longitudinal solitary wave propagation is found for potentials associated w...

The water wave generation by wave paddle and a freely falling rigid body are examined by using an Incompressible Smoothed Particle Hydrodynamics (ISPH). In the current ISPH method, the pressure was evaluated by solving pressure Poisson equation using a semi-implicit algorithm based on the projection scheme and the source term of pressure Poisson equation contains both of divergence free velocit...

We study the spectral (in)stability of one-dimensional solitary and cnoidal waves of various Boussinesq systems. These systems model three-dimensional water waves (i.e., the surface is two-dimensional) with or without surface tension. We present the results of numerous computations examining the spectra related to the linear stability problem for both stationary solitary and cnoidal waves with ...

In this paper, the modified exp-function method is used to seek generalized wave solutions of Klein-Gordon equation. As a result, some new types of exact traveling wave solutions are obtained which include kink wave solutions, periodic wave solution, and solitary wave solutions. Obtained results clearly indicate the reliability and efficiency of the proposed modified exp-function method.

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...

An explanation is given for previous numerical results which suggest a certain bifurcation of ‘vector solitons’ from scalar (single-component) solitary waves in coupled nonlinear Schrödinger (NLS) systems. The bifurcation in question is nonlocal in the sense that the vector soliton does not have a small-amplitude component, but instead approaches a solitary wave of one component with two infini...

Embedded solitons are solitary waves residing inside the continuous spectrum of a wave system. They have been discovered in a wide array of physical situations recently. In this article, we present the first comprehensive theory on the dynamics of embedded solitons and nonlocal solitary waves in the framework of the perturbed fifth-order Korteweg–de Vries (KdV) hierarchy equation. Our method is...