Related papers: Higher-order corrections to the short-pulse equati…

The generation of finite energy packets of X-waves is analysed in normally dispersive cubic media by using an X-wave expansion. The 3D nonlinear Schroedinger model is reduced to a 1D equation with anomalous dispersion. Pulse splitting and…

This paper probes the dispersive shock waves (DSWs) theory in nonlinear optical systems through Whitham modulation theory for the high-order Chen-Lee-Liu (HOCLL) equation. We systematically derived the one-phase periodic solutions and the…

It is known that a nonlinear Schr\"odinger equation describes the self-modulation of a large amplitude circularly polarized wave in relativistic electron-positron plasmas in the weakly and strongly magnetized limits. Here, we show that such…

We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists in a 1+1D generalized nonlinear Schr\"odinger equation with a periodic nonlinear…

For the short pulse initial data with a first order outgoing constraint condition and optimal orders of smallness, we establish the global existence of smooth solutions to 2D quasilinear wave equations with higher order null conditions.…

In this work, we perform a detailed review about the theoretical modeling of the optical propagation of ultra-short pulses in different scenarios of nonlinear optics. In particular, we focus our efforts on optical fibers and uniform media,…

We consider the simplest instabilities involving multiple unstable electrostatic plasma waves corresponding to four-dimensional systems of mode amplitude equations. In each case the coupled amplitude equations are derived up to third order…

For nonlinear wave equations with a potential term we prove pointwise space-time decay estimates and develop a perturbation theory for small initial data. We show that the perturbation series has a positive convergence radius by a method…

We consider the focusing energy-critical quintic nonlinear wave equation in three dimensional Euclidean space. It is known that this equation admits a one-parameter family of radial stationary solutions, called solitons, which can be viewed…

The iteration sequence based on the BLUES (Beyond Linear Use of Equation Superposition) function method for calculating analytic approximants to solutions of nonlinear ordinary differential equations with sources is elaborated upon. Diverse…

In this work we generalize the models for nonlinear waves in a gas--liquid mixture taking into account an interphase heat transfer, a surface tension and a weak liquid compressibility simultaneously at the derivation of the equations for…

We prove that the short-pulse equation, which is derived from Maxwell equations with formal asymptotic methods, can be rigorously justified. The justification procedure applies to small-norm solutions of the short-pulse equation. Although…

We present a framework for constructing a first-order hyperbolic system whose solution approximates that of a desired higher-order evolution equation. Constructions of this kind have received increasing interest in recent years, and are…

In this paper we study the long time behavior for a semilinear wave equation with space-dependent and nonlinear damping term. After rewriting the equation as a first order system, we define a class of approximate solutions that employ…

We consider three novel PDEs associated with the integrable generalizations of the short pulse equation classified recently by Hone {\it et al} (2018 {\it Lett. Math. Phys.} {\bf 108} 927-947). In particular, we obtain a variety of exact…

The before described general principles and methodology of calculating electron wave propagation in homogeneous isotropic half-infinity slab of Maxwellian plasma with indefinite but in principal value sense taken integrals in characteristic…

It is well recognized that new types of exact travelling wave solutions to nonlinear partial differential equations can be obtained by modifications of the methods which are in hand. In this study, we extend the class of auxiliary equations…

The article first studies the propagation of well prepared high frequency waves with small amplitude $\eps$ near constant solutions for entropy solutions of multidimensional nonlinear scalar conservation laws. Second, such oscillating…

In this paper, we study a compound Korteweg-de Vries-Burgers equation with a higher-order nonlinearity. A class of solitary wave solutions is obtained by means of a series expansion.

As an application of Gradient Expansion (long-wavelength) approximation, we studied the inhomogeneous universe including the gravitational wave(GW). For a plane-symmetric cosmological model, we could implement the 2nd order expansion and…