Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation

For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.

混油钻井液中地层油的T1-T2二维核磁共振识别与评价方法

混油钻井液影响地层含油性的实时发现与准确评价,色谱、质谱、光谱等扣除背景值的识别方法定量精度较低,一维核磁共振方法需要在添加弛豫试剂前、后进行2次分析,为此采用T1-T2二维核磁共振测量方法,通过对混油钻井液、不同矿化度盐水及3种成品油、5种原油的测试,建立了混油钻井液中的水、基础油、地层油的解释图版;通过对混油钻井液均匀混入不同含量原油后的测试,建立了混油钻井液中的地层油含量评价模型;通过不同质量白油的测试,确定了T1-T2的检测下限为200~750 mg/L。经实验模拟及实钻验证,所建立的解释图版和评价模型可靠。因此,T1-T2二维核磁共振能够直接、直观区分混油钻井液中的基础油和地层油,实现地层含油性的及时发现与直观识别。

用反讽打造多维空间--评《10 1/2章世界史》

在《10 1/2章世界史》中,朱利安·巴恩斯在四个层面上用反讽打造该作品的多维空间格局,展现作品的复调意义:在结构和叙述模式层面上对正史进行戏仿;用重复的意象否定历史的进步性;在单个故事内部通过语言的不充分性展现相互质疑、相互对话的观念;从形而上的高度用全书否定解决矛盾的可能性。巴恩斯一面用反讽反抗主流权威话语,否定现实世界;一面用反讽质疑终极真理价值,否定理想世界。这部作品多维空间的建构隐喻和象征了世界的复杂性和人类生存的荒谬性。反讽既是画笔,又是巴恩斯对抗荒谬探求个人和共同体生存意义的武器。

The Travelling Wave Solutions for （2＋1）-dimensional AKNS Equation

Based on the travelling wave method, a(2 + 1)-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic solution. It also proves that the result is consistent with the soliton solution of simplify Hirota bilinear method by Wazwaz and illustrate the solution are right travelling wave solution.

Exotic interactions between solitons of the （2＋1）-dimensional asymmetric Nizhnik-Novikov-Veselov system

Starting from the extended tanh-function method （ETM） based on the mapping method, the variable separation solutions of the （2＋1）-dimensional asymmetric Nizhnik Novikov Veselov （ANNV） system are derived. By further study, we find that these variable separation solutions are seemingly independent of but actually dependent on each other. Based on the variable separation solution and by choosing appropriate functions, some novel and interesting interactions between special solitons, such as bell-like compacton, peakon-like compacton and compacton-like semifoldon, are investigated.

Modified (2+1)-dimensional displacement shallow water wave system and its approximate similarity solutions

Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS （M2DDSWWS） is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.

Nonlocal symmetry and exact solutions of the(2+1)-dimensional modified Bogoyavlenskii–Schiff equation

In this paper,the truncated Painlev′e analysis,nonlocal symmetry,Bcklund transformation of the（2＋1）-dimensional modified Bogoyavlenskii–Schiff equation are presented.Then the nonlocal symmetry is localized to the corresponding nonlocal group by the prolonged system.In addition,the（2＋1）-dimensional modified Bogoyavlenskii–Schiff is proved consistent Riccati expansion（CRE） solvable.As a result,the soliton–cnoidal wave interaction solutions of the equation are explicitly given,which are difficult to find by other traditional methods.Moreover figures are given out to show the properties of the explicit analytic interaction solutions.

New periodic wave solutions, localized excitations and their interaction for (2+1)-dimensional Burgers equation

Based on the B/icklund method and the multilinear variable separation approach （MLVSA）, this paper finds a general solution including two arbitrary functions for the （2＋1）-dimensional Burgers equations. Then a class of new doubly periodic wave solutions for （2＋l）-dimensional Burgers equations is obtained by introducing appropriate Jacobi elliptic functions, Weierstrass elliptic functions and their combination in the general solutions （which contains two arbitrary functions）. Two types of limit cases are considered. Firstly, taking one of the moduli to be unity and the other zero, it obtains particular wave （called semi-localized） patterns, which is periodic in one direction, but localized in the other direction. Secondly, if both moduli are tending to 1 as a limit, it derives some novel localized excitations （two-dromion solution）.

The exact solutions to (2+1)-dimensional nonlinear Schrdinger equation

By using the extended F-expansion method, the exact solutions,including periodic wave solutions expressed by Jacobi elliptic functions, for (2+1)-dimensional nonlinear Schrdinger equation are derived. In the limit cases, the solitary wave solutions and the other type of traveling wave solutions for the system are obtained.

New exact periodic solutions to (2+1)-dimensional dispersive long wave equations

In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for （2＋1）-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions （m → 1）. This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.

Nonlocal symmetries,consistent Riccati expansion integrability,and their applications of the (2+1)-dimensional Broer–Kaup–Kupershmidt system

For the （2＋1）-dimensional Broer–Kaup–Kupershmidt（BKK） system, the nonlocal symmetries related to the Schwarzian variable and the corresponding transformation group are found. Moreover, the integrability of the BKK system in the sense of having a consistent Riccati expansion（CRE） is investigated. The interaction solutions between soliton and cnoidal periodic wave are explicitly studied.

Exact solutions of a(2+1)-dimensional extended shallow water wave equation

We give the bilinear form and n-soliton solutions of a（2+1）-dimensional [（2+1）-D] extended shallow water wave（eSWW） equation associated with two functions v and r by using Hirota bilinear method. We provide solitons, breathers,and hybrid solutions of them. Four cases of a crucial φ（y）, which is an arbitrary real continuous function appeared in f of bilinear form, are selected by using Jacobi elliptic functions, which yield a periodic solution and three kinds of doubly localized dormion-type solution. The first order Jacobi-type solution travels parallelly along the x axis with the velocity（3k12+ α, 0） on（x, y）-plane. If φ（y） = sn（y, 3/10）, it is a periodic solution. If φ（y） = cn（y, 1）, it is a dormion-type-Ⅰ solutions which has a maximum（3/4）k1p1 and a minimum-（3/4）k1p1. The width of the contour line is ln■. If φ（y） = sn（y, 1）, we get a dormion-type-Ⅱ solution（26） which has only one extreme value-（3/2）k1p1. The width of the contour line is ln■. If φ（y） = sn（y, 1/2）/（1 + y2）, we get a dormion-type-Ⅲ solution（21） which shows very strong doubly localized feature on（x, y） plane. Moreover, several interesting patterns of the mixture of periodic and localized solutions are also given in graphic way.

Painlevé Property and Exact Solutions to a (2+1) Dimensional KdV-mKdV Equation

A (2 + 1) dimensional KdV-mKdV equation is proposed and integrability in the sense of Painlevé and some exact solutions are discussed. The B?cklund transformation and bilinear equations are obtained through Painlevé analysis. Some exact solutions are deduced by Hirota method and generalized Wronskian method.

New Exact Solutions of the (2 + 1)-Dimensional AKNS Equation

N-soliton solutions and the bilinear form of the (2 + 1)-dimensional AKNS equation are obtained by using the Hirota method. Moreover, the double Wronskian solution and generalized double Wronskian solution are constructed through the Wronskian technique. Furthermore, rational solutions, Matveev solutions and complexitons of the (2 + 1)-dimensional AKNS equation are given through a matrix method for constructing double Wronskian entries. The three solutions are new.

Solving (2+1)-dimensional sine-Poisson equation by a modified variable separated ordinary differential equation method

By introducing a more general auxiliary ordinary differential equation （ODE）, a modified variable separated ordinary differential equation method is presented for solving the （2 ＋ 1）-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the （2 ＋ 1）-dimensional sine-Poisson equation are derived in a simple manner by this technique.

New Exact Traveling Wave Solutions of (2 + 1)-Dimensional Time-Fractional Zoomeron Equation

In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the conformable fractional derivative. As a result, the singular soliton solutions, kink and anti-kink soliton solutions, periodic function soliton solutions, Jacobi elliptic function solutions and hyperbolic function solutions of (2 + 1)-dimensional time-fractional Zoomeron equation were obtained. Finally, the 3D and 2D graphs of some solutions were drawn by setting the suitable values of parameters with Maple, and analyze the dynamic behaviors of the solutions.

Symmetry and Similarity Solutions of a （2＋1）-Dimensional Generalized Broer-Kaup System

We study the symmetries of a （2＋1）-dimensional generalized Broer-Kaup system by means of the classical Lie group theory. The corresponding group algebra is constructed. Based on the symmetries, severaJ types of similarity solutions are obtained.

1T′‐MoTe_(2) monolayer:A promising two‐dimensional catalyst for the electrochemical production of hydrogen peroxide

The direct synthesis of hydrogen peroxide(H_(2)O_(2))via a two‐electron oxygen reduction reaction(2e‐ORR)in acidic media has emerged as a green process for the production of this valuable chemical.However,such an approach employs expensive noble‐metal‐based electrocatalysts,which severely undermines its feasibility when implemented on an industrial scale.Herein,based on density functional theory computations and microkinetic modeling,we demonstrate that a novel two‐dimensional(2D)material,namely a 1T′‐MoTe_(2)monolayer,can serve as an efficient non‐precious electrocatalyst to facilitate the 2e‐ORR.The 1T′‐MoTe_(2)monolayer is a stable 2D crystal that can be easily produced through exfoliation techniques.The surface‐exposed Te sites of the 1T′‐MoTe_(2)monolayer exhibit a favorable OOH*binding energy of 4.24 eV,resulting in a rather high basal plane activity toward the 2e‐ORR.Importantly,kinetic computations indicate that the 1T'‐MoTe_(2)monolayer preferentially promotes the formation of H_(2)O_(2)over the competing four‐electron ORR step.These desirable characteristics render 1T′‐MoTe_(2)a promising candidate for catalyzing the electrochemical reduction of O_(2)to H_(2)O_(2).

Wronskian and Grammian solutions for the(2+1)-dimensional BKP equation

The （2＋1）-dimensional BKP equation in the Hirota bilinear form is studied during this work. Wronskian and Grammian techniques are applied to the construction of Wronskian and Grammian solutions of this equation, respectively. It is shown that these solutions can be expressed as not only Pfaffians but also Wronskians and Grammians.

A(2+1)-Dimensional Dispersive Long Wave Hierarchy and its Integrable Couplings

Under the frame of the (2+1)-dimensional zero curvature equation and Tu model, the (2+1)-dimensional dispersive long wave hierarchy is obtained. Furthermore, the loop algebra is expanded into a larger one. Moreover, a class of integrable coupling system for dispersive long wave hierarchy and (2+1)-dimensional multi-component integrable system will be investigated.