关于近岸波浪几个问题的讨论

本文利用流体动力学方法,采取确定的函数,讨论了近岸波浪的非色散性、波浪质点的运动规律及水面波的运动规迹。

Nonpropagating Solitons in （2＋1）-Dimensional Dispersive Long-Water Wave System

With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc.are revealed by selecting appropriate functions in this paper.

New Symmetry Reductions,Dromions—Like and Compacton Solutions for a 2D BS（m,n） Equations Hierarchy with Fully Nonlinear Dispersion

We have found two types of important exact solutions, compacton solutions, which are solitary waves with the property that after colliding with their own kind, they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction, in the and even models, and dromion solutions (exponentially decaying solutions in all direction) in many and models. In this paper, symmetry reductions in are considered for the break soliton-type equation with fully nonlinear dispersion (called equation) , which is a generalized model of break soliton equation , by using the extended direct reduction method. As a result, six types of symmetry reductions are obtained. Starting from the reduction equations and some simple transformations, we obtain the solitary wave solutions of equations, compacton solutions of equations and the compacton-like solution of the potential form (called ) . In addition, we show that the variable admits dromion solutions rather than the field itself in equation.

New Soliton Solutions with Compact Support for a Family of Two—Parameter Regularized Long—Wave Boussinesq Equations

Searching for special solitary wave solutions with compact support is of important significance in soliton theory. In this paper, to understand the role of nonlinear dispersion in pattern formation, a family of the regularized long-wave Boussinesq equations with fully nonlinear dispersion (simply called equations), ( const.), is studied. New solitary wave solutions with compact support of equations are found. In addition we find another compacton solutions of the two special cases, equation and equation. It is found that the nonlinear dispersion term in a nonlinear evolution equation is not a necessary condition of that it possesses compacton solutions.

Nonlinear Propagation of Coupling Optical Pulse under Compton Scattering in Laser Medium

After considering Kerr nonlinear effect, group velocity dispersion of host and gain distribution of active particle in laser amplifying medium, a basic equation describing propagation of the coupling optical pulse under the multi-photon nonlinear Compton scattering in the laser amplifying medium has been deduced. Besides, the profile and power spectrum of a picosecond-level super-Gaussian coupling pulse in the laser amplifying medium have been discussed when its central frequency coincides with the gain peak frequency of the laser amplifying medium.

Fractal Dromion,Fractal Lump,and Multiple peakon Excitations in a New （2＋1）—Dimensional Long Dispersive Wave SYstem

By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: is derived. Some types of the usual localized excitations such as dromions, lumps, rings, and oscillating soliton excitations can be easily constructed by selecting the arbitrary functions appropriately. Besides these usual localized structures, some new localized excitations like fractal-dromion, fractal-lump, and multi-peakon excitations of this new system are found by selecting appropriate functions.

New Compacton Solutions and Solitary Pattern Solutions for Modified Nonlinearly Dispersive mK(m,n,a,b) Equation

In this paper exact solutions of a new modified nonlinearly dispersive equation （simply called inK（m, n, a, b） Ua Ub equation）, u^m-1 ut ＋ α（ u^n）x ＋β（u^a（u^b）xx）x = 0, is investigated by using some direct algorithms. As a result, abundant new compacton solutions （solitons with the absence of infinite wings） and solitary pattern solutions （having infinite slopes or cusps） are obtained.

New Exact Travelling Wave Solutions for Zakharov-Kuznetsov Equation

In this paper, the nonlinear dispersive Zakharov- Kuznetsov equation is solved by using the generalized auxiliary equation method. As a result, new solitary pattern, solitary wave and singular solitary wave solutions are found.

Generation of Flat Supercontinuum in a Single-mode Optical Fiber with a Convex Chromatic Dispersion Profile

A single-mode optical fiber with a convex chromatic dispersion profile is proposed for generating a flat supercontinuum(SC).The fiber has normal dispersion and the dispersion parameter D(λ,z) is a convex function of wavelengths.It is shown from the numerical results that the chromatic dispersion,the flatness of the dispersion curve and the pump conditions have significant effect on SC generation.A flat and broad SC without strong residual pump component can be obtained when the pump wavelength is set in the vicinity of the wavelength at which the fiber has small normal group-velocity dispersion(GVD) and small dispersion slope.The fiber with a smaller normal GVD,a flatter dispersion profile and a higher nonlinear coefficient are more suitable for broad SC generation.

Effect of an Arbitrary Dust Size Distribution Dust Particles for Vortex-Like Ion Distribution Dusty Plasma

In order to investigate the effect of an arbitrary dust size distribution for vortex-like ion distributiondusty plasma,we use a reasonable polynomial-expressed function to represent an arbitrary dust size distribution.Thenumerical results of linear dispersion relation,nonlinear solitary wave amplitude,width and velocity for polynomialexpressed dust size distribution dusty plasma with vortex-like ion distribution have been studied.

Pulse Amplification in Dispersion-Decreasing Fibers with Symbolic Computation

The pulse amplification in the dispersion-decreasing fiber （DDF） is investigated via symbolic computation to solve the variable-coefficient higher-order nonlinear Schrfdinger equation with the effects of third-order dispersion, self-steepening, and stimulated Raman scattering. The analytic one-soliton solution of this model is obtained with a set of parametric conditions. Based on this solution, the fundamental soliton is shown to be amplified in the DDF. The comparison of the amplitude of pulses for different dispersion profiles of the DDF is also performed through the graphical analysis. The results of this paper would be of certain value to the study of signal amplification and pulse compression.

Modelling the Resonance of Infragravity Waves in Port Areas

This paper deals with linear refraction-difractional and nonlinear dispersion mathematical models for simulation of low-frequency waves in port areas of various configurations. The phenomenon of resonance can be observed in multiple places and pose a significant danger for ships and constructions. Generally, if the bottom relief is non-uniform and if inner/outer boundaries of protected areas are configurated in a complex way, the problem can be solved only by numerical methods. It presents the calculation results for the amplitude of infragravity waves at resonance frequencies. The paper highlights the solutions for diminishing the amplitude of resonance water fluctuations in port areas. In particular, it is noted that if a number of certain conditions is provided outside the protected area, it is possible to diminish substantially the height of infragravity waves inside the area. The validity of such an assumption is confirmed by calculations.

Green-Naghdi Theory,Part A:Green-Naghdi(GN) Equations for Shallow Water Waves

In this work, Green-Naghdi （GN） equations with general weight functions were derived in a simple way. A wave-absorbing beach was also considered in the general GN equations. A numerical solution for a level higher than 4 was not feasible in the past with the original GN equations. The GN equations for shallow water waves were simplified here, which make the application of high level （higher than 4） equations feasible. The linear dispersion relationships of the first seven levels were presented. The accuracy of dispersion relationships increased as the level increased. Level 7 GN equations are capable of simulating waves out to wave number times depth kd 〈 26. Numerical simulation of nonlinear water waves was performed by use of Level 5 and 7 GN equations, which will be presented in the next paper.

Further Extended Jacobi Elliptic Function Rational Expansion Method and New Families of Jacobi Elliptic Function Solutions to （2＋1）-Dimensional Dispersive Long Wave Equation

In this paper, a further extended Jacobi elliptic function rationM expansion method is proposed for constructing new forms of exact solutions to nonlinear partial differential equations by making a more general transformation. For illustration, we apply the method to （2＋1）-dimensionM dispersive long wave equation and successfully obtain many new doubly periodic solutions. When the modulus m→1, these sohitions degenerate as soliton solutions. The method can be also applied to other nonlinear partial differential equations.

Strongly nonlinear long interfacial waves in uniform basic flows and their dispersion relationship

In this paper, long interfacial waves of finite amplitude in uniform basic flows are considered with the assumption that the aspect ratio between wavelength and water depth is small. A new model is derived using the velocities at arbitrary distances from the still water level as the velocity variables instead of the commonly used depth-averaged velocities. This significantly improves the dispersion properties and makes them applicable to a wider range of water depths. Since its derivation requires no assumption on wave amplitude, the model thus can be used to describe waves with arbitrary amplitude.

New Extended Jacobi Elliptic Function Rational Expansion Method and Its Application

In this paper, an extended Jacobi elliptic function rational expansion method is proposed for constructing new forms of exact Jacobi elliptic function solutions to nonlinear partial differential equations by means of making a more general transformation. For illustration, we apply the method to the （2＋1）-dimensional dispersive long wave equation and successfully obtain many new doubly periodic solutions, which degenerate as soliton solutions when the modulus m approximates 1. The method can also be applied to other nonlinear partial differential equations.

Painlev Analysis,Lie Symmetries and Exact Solutions for Variable Coefficients Benjamin-Bona-Mahony-Burger (BBMB) Equation

In this paper, a variable-coefficient Benjarnin-Bona-Mahony-Burger （BBMB） equation arising as a math- ematical model of propagation of small-amplitude long waves in nonlinear dispersive media is investigated. The inte- grability of such an equation is studied with Painlevd analysis. The Lie symmetry method is performed for the BBMB equation and then similarity reductions and exact solutions are obtained based on the optimal system method. Further- more different types of solitary, periodic and kink waves can be seen with the change of variable coefficients.

Dispersive Blow-Up Ⅱ.Schrdinger-Type Equations,Optical and Oceanic Rogue Waves

Addressed here is the occurrence of point singularities which owe to the focusing of short or long waves, a phenomenon labeled dispersive blow-up. The context of this investigation is linear and nonlinear, strongly dispersive equations or systems of equations. The present essay deals with linear and nonlinear Schrdinger equations, a class of fractional order Schrdinger equations and the linearized water wave equations, with and without surface tension. Commentary about how the results may bear upon the formation of rogue waves in fluid and optical environments is also included.

Rogue Waves of the Higher-Order Dispersive Nonlinear Schrdinger Equation

In this paper,the rogue waves of the higher-order dispersive nonlinear Schrdinger(HDNLS) equation are investigated,which describes the propagation of ultrashort optical pulse in optical fibers.The rogue wave solutions of HDNLS equation are constructed by using the modified Darboux transformation method.The explicit first and secondorder rogue wave solutions are presented under the plane wave seeding solution background.The nonlinear dynamics and properties of rogue waves are discussed by analyzing the obtained rational solutions.The influence of little perturbation on the rogue waves is discussed with the help of graphical simulation.

Novel design of highly nonlinear photonic crystal fibers with flattened dispersion

Novel highly nonlinear photonic crystal fibers(HN-PCFs) with flattened dispersion are proposed by omitting 19 air holes as the fiber core.The simulation results show that the high nonlinearity and the flattened dispersion can be achieved simultaneously by employing only two types of air holes in the cladding.To reduce the confinement loss,the modified designs are presented.The confinement loss is below 0.1 dB/km at 1.55 μm,when seven layers of air-hole rings are introduced to the cladding.After modifying,the dispersion can change from-0.5 ps/(nm.km) to+0.5 ps/(nm.km) in the range from 1.35 μm to 2.06 μm,and the effective mode area is as low as 2.27 μm 2 at 1.55 μm.