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.

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.

Exact travelling wave solutions for （1＋ 1）-dimensional dispersive long wave equation

A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a （1＋1）-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems.

Insulin like growth factor-1 increases fatty liver preservation in IGL-1 solution

AIM: To investigate the benefits of insulin like growth factor-1 (IGF-1) supplementation to serum-free institut georges lopez-1 (IGL-1) solution to protect fatty liver against cold ischemia reperfusion injury. METHODS: Steatotic livers were preserved for 24 h in IGL-1  solution supplemented with or without IGF-1 and then perfused "ex vivo " for 2 h at 37℃. We examined the effects of IGF-1 on hepatic damage and function (transaminases, percentage of sulfobromophthalein clearance in bile and vascular resistance). We also studied other factors associated with the poor tolerance of fatty livers to cold ischemia reperfusion injury such as mitochondrial damage, oxidative stress, nitric oxide, tumor necrosis factor-α (TNF-α) and mitogen-activated protein kinases.RESULTS: Steatotic livers preserved in IGL-1 solutionsupplemented with IGF-1 showed lower transaminase levels, increased bile clearance and a reduction in vascular resistance when compared to those preserved in IGL-1solution alone. These benefits are mediated by activation of AKT and constitutive endothelial nitric oxide synthase (eNOS), as well as the inhibition of inflammatory cytokines such as TNF-α. Mitochondrial damage and oxidative stress were also prevented.CONCLUSION: IGL-1  enrichment with IGF-1 increasedfatty liver graft preservation through AKT and eNOS activation, and prevented TNF-α release during normothermic reperfusion.

The (G'/G, 1/G)-expansion method and its application to travelling wave solutions of the Zakharov equations

The （G＇/G, 1/G）-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the （G＇/G）-expansion method proposed recently, is presented. By using this method abundant travelling wave so- lutions with arbitrary parameters of the Zakharov equations are successfully obtained. When the parameters are replaced by special values, the well-known solitary wave solutions of the equations are rediscovered from the travelling waves.

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.

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.

Grammian Determinant Solution and Pfaffianization for a (3+1)-Dimensional Soliton Equation

Based on the Pfaffian derivative formulae,a Grammian determinant solution for a(3+1)-dimensionalsoliton equation is obtained.Moreover,the Pfaffianization procedure is applied for the equation to generate a newcoupled system.At last,a Gram-type Pfaffian solution to the new coupled system is given.

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）.

A more general form of lump solution,lumpoff,and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation

In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution.

All Single Traveling Wave Solutions to （3＋1）-Dimensional Nizhnok-Novikov-Veselov Equation

Using elementary integral method, a complete classification of all possible exact traveling wave solutions to （3＋1）-dimensional Nizhnok-Novikov-Veselov equation is given. Some solutions are new.

Wronskian and Grammian Solutions for(2+1)-Dimensional Soliton Equation

In this paper, the （2＋ 1）-dimensional soliton equation is mainly being discussed. Based on the Hirota direct method, Wronskian technique and the Pfattlan properties, the N-soliton solution, Wronskian and Grammian solutions have been generated.

Evaluation of IGL-1 preservation solution using an orthotopic liver transplantation model

AIM： To compare, in a pig the protective effect of UW liver transplantation model, with that of IGL-1, a highsodium preservation solution containing polyethylene glycol （PEG） as an oncotic supply. METHODS： All livers were harvested and grafted orthotopically according to standard techniques. The livers were washed out and preserved for 7 h in IGL-1 （n = 6） or in UW solution （n = 7） at 4℃. In a sham group （n = 4）, the livers underwent a 60-min warm ischemia at 37℃. The hepatocellular injury was assessed in organ preservation solution washed out from the graft at the end of ischemic storage （before revascularization）, and in serum 2 h after reperfusion and daily for up to 6 d. RESULTS： Livers preserved in IGL-1 solution released markedly less AST than that preserved in the UW solution before and after revascularization （P 〈 0.05）. Besides, the activity of creatine kinase-BB, a marker of sinusoidal lining cells injury, was higher in the UW group than in the IGL-1 group （P 〈 0.05）. Histological results showed less necrotic regions in livers preserved in IGL-1 solution; however, no difference was observed for inflammation. CONCLUSION： IGL-1 liquid effectively protects parenchymal and non-parenchymal cells against preservation-reperfusion injuries.

Clinical study of applying fructose-1,6-diphosphate and captopril to enhance the protective effects of cardioplegia solution on ischemic myocardium

In the present experiment,fructose-1,6-diphosphate（FDP）and captopril（Cap）wereadded to the cold potassium cardioplegia solution and the levels of malondialdehyde（MDA）,cre-atine phosphokinase MB（CPK-MB）,thromboxane B（TXB2）and 6-keto-PGF1α in plasma weremeasured during open-heart surgery.Quantitative study of myocardial ultrastructure and obser-vation of cardiac resuscitation were also undertaken.The findings suggested that FDP,especiallywhen combined with Cap could significantly strengthen the protective effects of cold potassiumcardioplegia solution on ischemic myocardium.

New Exact Solutions and Conservation Laws to （3＋1）-Dimensional Potential-YTSF Equation

Using the modified find some new exact solutions to Lie point symmetry groups and also get conservation laws, of the CK＇s direct method, we build the relationship between new solutions and old ones and the （3＋1）-dimensional potentiaial-YTSF equation. Baaed on the invariant group theory, Lie symmetries of the （3＋1）-dimensional potential-YTSF equation are obtained. We equation with the given Lie symmetry.

Synthesis and thermoelectric properties of Mg_2Si_(1-x)Sn_x solid solutions by microwave irradiation

In order to reduce the oxidizing and volatilizing caused by Mg element in the traditional methods for synthesizing Mg2Sil-xSnx （x=0.2, 0.4, 0.6, 0.8） solid solutions, microwave irradiation techniques were used in preparing them as thermoelectric materials. Structure and phase composition of the obtained materials were investigated by X-ray diffraction （XRD）. The electrical conductivity, Seebeck coefficient and thermal conductivity were measured as a function of temperature from 300 to 750 K. It is found that Mg2Si1-xSnx solid solutions are well formed with excessive content of 5% （molar fraction） Mg from the stoichiometric MgESil.xSnx under microwave irradiation. A maximum dimensionless figure of merit, ZT, of about 0.26 is obtained for Mg2Si1-xSnx solid solutions at about 500 K for x=0.6.

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.

A New Rational Algebraic Approach to Find Exact Analytical Solutions to a （2＋1）-Dimensional System

In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions. The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions, and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on （2＋1）-dimensional dispersive long-wave equation.