Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation

This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.

MOLECULES AND NEW INTERACTIONAL STRUCTURES FOR A(2+1)-DIMENSIONAL GENERALIZED KONOPELCHENKO-DUBROVSKY-KAUP-KUPERSHMIDT EQUATION

Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmetric solitons upon assigning appropriate values to some parameters.Furthermore,a double-peaked lump solution can be constructed with breather degeneration approach.By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions,various kinds of interactional structures are constructed;There include the soliton molecule(SM),the breather molecule(BM)and the soliton-breather molecule(SBM).Graphical investigation and theoretical analysis show that the interactions composed of SM,BM and SBM are inelastic.

Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the(2+1)-dimensional elliptic Toda equation

The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions between two breathers,a breather/lump and line solitons as well as lump molecules for the(2+1)-dimensional elliptic Toda equation.Based on the N-soliton solution,we obtain the hybrid solutions consisting of line solitons,breathers and lumps.Through the asymptotic analysis of these hybrid solutions,we derive the phase shifts of the breather,lump and line solitons before and after the interaction between a breather/lump and line solitons.By making the phase shifts infinite,we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons.Through the asymptotic analysis of these resonant solutions,we demonstrate that the resonant interactions exhibit the fusion,fission,time-localized breather and rogue lump phenomena.Utilizing the velocity resonance method,we obtain lump–soliton,lump–breather,lump–soliton–breather and lump–breather–breather molecules.The above works have not been reported in the(2+1)-dimensional discrete nonlinear wave equations.

Interaction solutions and localized waves to the(2+1)-dimensional Hirota-Satsuma-Ito equation with variable coefficient

This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé analysis.On the basis of the bilinear form,the forms of two-soliton solutions,three-soliton solutions,and four-soliton solutions are studied specifically.The appropriate parameter values are chosen and the corresponding figures are presented.The breather waves solutions,lump solutions,periodic solutions and the interaction of breather waves solutions and soliton solutions,etc.are given.In addition,we also analyze the different effects of the parameters on the figures.The figures of the same set of parameters in different planes are presented to describe the dynamical behavior of solutions.These are important for describing water waves in nature.

基于恒定梯度编码一维选层T_(2)谱的胶结砂岩层析成像方法

核磁共振成像是探究岩心尺度非均质性的先进技术,受岩石复杂性和编码技术影响,现有方法效果不佳。基于梯度场的二维/三维核磁共振技术成像容易但信噪比低,无梯度场的传统选层T_(2)谱(频率编码/相位编码)方法效率低。该研究提出恒定梯度编码一维选层T_(2)谱层析成像方法,做到了成像数据体量小、信噪比高且信号更完整。层析T_(2)谱图像及其热度分布,能够有效表征毛细管压力和成岩作用对流体非均匀分布的影响。饱和油状态时,T_(2)谱层间差异性反映成岩作用影响。高饱和油阶段,轴向热度图反映了低毛细管压力游离油的脱出规律。完全驱替后毛细管压力进入稳定状态,轴向热度图反映了微孔中吸附油赋存状态的差异。该技术在胶结砂岩气驱油实验中取得了良好效果,并对解析强非均质岩石渗流规律有重要作用。

A bi-functional strategy involving surface coating and subsurface gradient co-doping for enhanced cycle stability of LiCoO_(2) at 4.6 V

Layered LiCoO_(2)(LCO)acts as a dominant cathode material for lithium-ion batteries(LIBs)in 3C products because of its high compacted density and volumetric energy density.Although improving the high cutoff voltage is an effective strategy to increase its capacity,such behavior would trigger rapid capacity decay due to the surface or/and structure degradation.Herein,we propose a bi-functional surface strategy involving constructing a robust spinel-like phase coating layer with great integrity and compatibility to LiCoO_(2) and modulating crystal lattice by anion and cation gradient co-doping at the subsurface.As a result,the modified LiCoO_(2)(AFM-LCO)shows a capacity retention of 80.9%after 500 cycles between 3.0and 4.6 V.The Al,F,Mg enriched spinel-like phase coating layer serves as a robust physical barrier to effectively inhibit the undesired side reactions between the electrolyte and the cathode.Meanwhile,the Al,F,Mg gradient co-doping significantly enhances the surficial structure stability,suppresses Co dissolution and oxygen release,providing a stable path for Li-ions mobility all through the long-term cycles.Thus,the surface bi-functional strategy is an effective method to synergistically improve the electrochemical performances of LCO at a high cut-off voltage of 4.6 V.

Exotic Localized Coherent Structures of New (2+1)-Dimensional Soliton Equation

The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryfunctions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types ofsolutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functionsappropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the numberof the peaks.

A Variable Separation Approach to Solve the Integrable and Nonintegrable Models:Coherent Structures of the (2 + 1)-Dimensional KdV Eqnation

We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.

Role of 2-dimensional Doppler echo-cardiography in screening portopulmonary hypertension in portal hypertension patients

BACKGROUND: Portopulmonary hypertension (PPH) is difficult to recognize in the early and middle stages because it is frequently asymptomatic. As right ventricular function is impaired in patients with moderate and severe PPH, any dramatic hemodynamic changes in liver transplantation or other procedures may result in death from pulmonary and cardiac events. In this study, we investigated the prevalence of PPH in patients with portal hypertension (PHT) mainly caused by hepatitis B virus, and evaluated the effect of 2-dimensional Doppler echocardiography (2D-ECHO) in screening for PPH. METHODS: One hundred and five PHT patients received transthoracic 2D-ECHO preoperatively, systolic pulmonary arterial pressure (SPAP, normal range <30 mmHg) and pulmonary acceleration time (PAT, normal range >= 120 msec) were measured to screen for PPH (positive result: SPAP >= 30 mmHg and/or PAT <100 msec). Subsequently, pulmonary hemodynamic parameters were measured by right heart catheterization (RHC) for definitive diagnosis of PPH. The results of the two methods were compared to assess the screening effect of 2D-ECHO. RESULTS: The prevalence of PPH in this study was 3.8% (4/105). About 90% (95/105) of patients had a detectable tricuspid regurgitation by 2D-ECHO and the mean SPAP was 27.7 +/- 5.9 mmHg. Twenty-two of these 95 patients had an SPAP >30 mmHg. The mean PAT of all patients was 140 23 msec and 5 were <100 msec. Twenty-two patients were screened out by 2D-ECHO and 4 were diagnosed by RHC. A positive significant correlation (r=0.55, P<0.01) was found between SPAP measured by 2D-ECHO and mean pulmonary artery pressure (MPAP) measured by RHC, and a weak but significant negative correlation (r=-0.27, P=0.005) existed between PAT and pulmonary vascular resistance (PVR). The sensitivity, specificity, agreement rate, positive predictive value and negative predictive value of the screening test were 100%, 82%, 83%, 18% and 100%, respectively. CONCLUSIONS: The prevalence of PPH in this study is lower than in Western countries. As a screening test, 2D-ECHO has very high sensitivity and negative predictive value. A negative test result can directly be used to exclude PPH, while a positive result should be confirmed by RHC.

On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras

A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.

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.

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.

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）.

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 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.

Object-Based Burned Area Mapping with Extreme Gradient Boosting Using Sentinel-2 Imagery

The Sentinel-2 satellites are providing an unparalleled wealth of high-resolution remotely sensed information with a short revisit cycle, which is ideal for mapping burned areas both accurately and timely. This paper proposes an automated methodology for mapping burn scars using pairs of Sentinel-2 imagery, exploiting the state-of-the-art eXtreme Gradient Boosting (XGB) machine learning framework. A large database of 64 reference wildfire perimeters in Greece from 2016 to 2019 is used to train the classifier. An empirical methodology for appropriately sampling the training patterns from this database is formulated, which guarantees the effectiveness of the approach and its computational efficiency. A difference (pre-fire minus post-fire) spectral index is used for this purpose, upon which we appropriately identify the clear and fuzzy value ranges. To reduce the data volume, a super-pixel segmentation of the images is also employed, implemented via the QuickShift algorithm. The cross-validation results showcase the effectiveness of the proposed algorithm, with the average commission and omission errors being 9% and 2%, respectively, and the average Matthews correlation coefficient (MCC) equal to 0.93.

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(3k1^2+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[(2+√6+√2+√3)/(2+√6-√2-√3)]. 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[(√2+1)/(√2-1)]. If φ(y)= sn(y, 1/2)/(1 + y^2), 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.

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.

SiO_(2)掺杂量对SnO_(2)压敏电阻电气性能的影响

采用传统方法制备了掺杂不同物质的量分数(0.01%,0.05%,0.10%,0.15%,0.20%)SiO_(2)的SnO_(2)压敏电阻,研究了SiO_(2)掺杂量对SnO_(2)压敏电阻电气性能的影响。结果表明:随着SiO_(2)掺杂量的增加,SnO_(2)压敏电阻的电压梯度、非线性系数、势垒高度、施主密度和界面态密度均先增大后减小,泄漏电流密度先减小后增大,晶界电阻增大;当SiO_(2)物质的量分数为0.10%时,SnO_(2)压敏电阻的综合电气性能最佳,其电压梯度、非线性系数、施主密度、界面态密度、势垒高度最大,泄漏电流密度最小,分别为582 V·mm^(-1),33,1.7×10^(23)m-3,6.7×10^(16)m^(-2),2.03 eV,7.06μA·cm^(-2)。