Using one dimensional Quantum hydrodynamic (QHD) model Korteweg de Vries (KdV) solitary excitations of electron-acoustic waves (EAWs) have been examined in twoelectron-populated relativistically degenerate super dense plasma. It is found that relativistic degeneracy parameter influences the conditions of formation and properties of solitary structures. Keywords—Relativistic Degeneracy, Electron...

We discuss the solitary wave solutions of a particular two-component scalar field model in twodimensional Minkowski space. These solitary waves involve one, two or four lumps of energy. The adiabatic motion of these composite non-linear non-dispersive waves points to variations in shape.

We present new results for the time reversal of nonlinear pulses traveling in a random medium, in particular for solitary waves. We consider long water waves propagating in the presence of a spatially random depth. Both hyperbolic and dispersive regimes are considered. We demonstrate that in the presence of properly scaled stochastic forcing the solution to the nonlinear (shallow water) conserv...

The solitary waves that have been observed in the atmosphere fall broadly into two classes: those that propagate in a fairly shallow stratified layer near the ground and those that occupy the entire troposphere. We present a survey of the observations of both types of solitary waves. The generation mechanisms differ substantially for these two types of solitary waves. Those that propagate in a ...

We study the nonlinear equation i∂tψ = (√ −∆+m2 −m ) ψ − (|x| ∗ |ψ|)ψ on R, which is known to describe the dynamics of pseudo-relativistic boson stars in the meanfield limit. For positive mass parameters, m > 0, we prove existence of travelling solitary waves, ψ(t, x) = eφv(x− vt), with speed |v| < 1, where c = 1 corresponds to the speed of light in our units. Due to the lack of Lorentz covaria...

We study a Schrödinger-like equation with a nonlinear term. This nonlinearity has the effect of allowing the existence of highly concentrated stable solitary waves of a topological nature. Such solitary waves tend to move according to Bohmian mechanics. Therefore our model can be considered a nonsingular realization of de Broglie pilot wave theory.

The effect of phase-matched third-harmonic generation on the structure and stability of spatial solitary waves is investigated. A power threshold for the existence of two-frequency spatial solitons is found, and the multistability of solitary waves in a Kerr medium owing to a higher-order nonlinear phase shift caused by cascaded third-order processes is revealed.

This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady surface waves propagating in shallow water. We consider the (fully nonlinear, weakly dispersive) Serre–Green–Naghdi equations with surface tension, because it provides a tractable model that, in the same time, is not...

Oblique nonlinear interaction of two incident solitary waves, or soliton resonance, is important because it can produce a third solitary wave that has an amplitude up to 4 times the incident wave amplitude. Although this process is well studied for surface waves and in other fields of physics such as plasma, it has not been well studied for internal solitary-like waves (ISWs) in the ocean. In t...

We consider the solitary wave solutions of a Korteweg-de Vries equation, where the coefficients in the equation vary with time over a certain region. When these coefficients vary rapidly compared with the solitary wave, then it is well-known that the solitary wave may fission into two or more solitary waves. On the other hand, when these coefficients vary slowly, the solitary wave deforms adiab...