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.

Localization effect in single crystal of RuAs_(2)

We report the magnetotransport and thermal properties of RuAs_(2) single crystal.RuAs_(2) exhibits semiconductor behavior and localization effect.The crossover from normal state to diffusive transport in the weak localization(WL)state and then to variable range hopping(VRH)transport in the strong localization state has been observed.The transitions can be reflected in the measurement of resistivity and Seebeck coefficient.Negative magnetoresistance(NMR)emerges with the appearance of localization effect and is gradually suppressed in high magnetic field.The temperature dependent phase coherence length extracted from the fittings of NMR also indicates the transition from WL to VRH.The measurement of Hall effect reveals an anomaly of temperature dependent carrier concentration caused by localization effect.Our findings show that RuAs_(2) is a suitable platform to study the localized state.

Dynamics of Nonlinear Waves in(2+1)-Dimensional Extended Boiti-Leon-Manna-Pempinelli Equation

Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.

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.

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.

Selective CO_(2)Electroreduction to Multi-Carbon Products on Organic-Functionalized CuO Nanoparticles by Local Micro-Environment Modulation

Surface functionalization of Cu-based catalysts has demonstrated promising potential for enhancing the electrochemical CO_(2)reduction reaction(CO_(2)RR)toward multi-carbon(C2+)products,primarily by suppressing the parasitic hydrogen evolution reaction and facilitating a localized CO_(2)/CO concentration at the electrode.Building upon this approach,we developed surface-functionalized catalysts with exceptional activity and selectivity for electrocatalytic CO_(2)RR to C_(2+)in a neutral electrolyte.Employing CuO nanoparticles coated with hexaethynylbenzene organic molecules(HEB-CuO NPs),a remarkable C_(2+)Faradaic efficiency of nearly 90%was achieved at an unprecedented current density of 300 mA cm^(-2),and a high FE(>80%)was maintained at a wide range of current densities(100-600 mA cm^(-2))in neutral environments using a flow cell.Furthermore,in a membrane electrode assembly(MEA)electrolyzer,86.14%FEC2+was achieved at a partial current density of 387.6 mA cm^(-2)while maintaining continuous operation for over 50 h at a current density of 200 mA cm^(-2).In-situ spectroscopy studies and molecular dynamics simulations reveal that reducing the coverage of coordinated K⋅H2O water increased the probability of intermediate reactants(CO)interacting with the surface,thereby promoting efficient C-C coupling and enhancing the yield of C_(2+)products.This advancement offers significant potential for optimizing local micro-environments for sustainable and highly efficient C_(2+)production.

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.

Tailoring local structures of atomically dispersed copper sites for highly selective CO_(2) electroreduction

Atomically‐dispersed copper sites coordinated with nitrogen‐doped carbon(Cu–N–C)can provide novel possibilities to enable highly selective and active electrochemical CO_(2) reduction reactions.However,the construction of optimal local electronic structures for nitrogen‐coordinated Cu sites(Cu–N_(4))on carbon remains challenging.Here,we synthesized the Cu–N–C catalysts with atomically‐dispersed edge‐hosted Cu–N_(4) sites(Cu–N_(4)C_(8))located in a micropore between two graphitic sheets via a facile method to control the concentration of metal precursor.Edge‐hosted Cu–N_(4)C_(8) catalysts outperformed the previously reported M–N–C catalysts for CO_(2)‐to‐CO conversion,achieving a maximum CO Faradaic efficiency(FECO)of 96%,a CO current density of–8.97 mA cm^(–2) at–0.8 V versus reversible hydrogen electrode(RHE),and over FECO of 90%from–0.6 to–1.0 V versus RHE.Computational studies revealed that the micropore of the graphitic layer in edge‐hosted Cu–N_(4)C_(8) sites causes the d‐orbital energy level of the Cu atom to shift upward,which in return decreases the occupancy of antibonding states in the*COOH binding.This research suggests new insights into tailoring the locally coordinated structure of the electrocatalyst at the atomic scale to achieve highly selective electrocatalytic reactions.

Survival prognostic analysis of laparoscopic D2 radical resection for locally advanced gastric cancer: A multicenter cohort study

BACKGROUND With the development of minimally invasive surgical techniques,the use of laparoscopic D2 radical surgery for the treatment of locally advanced gastric cancer(GC)has gradually increased.However,the effect of this procedure on survival and prognosis remains controversial.This study evaluated the survival and prognosis of patients receiving laparoscopic D2 radical resection for the treatment of locally advanced GC to provide more reliable clinical evidence,guide clinical decision-making,optimize treatment strategies,and improve the survival rate and quality of life of patients.METHODS A retrospective cohort study was performed.Clinicopathological data from 652 patients with locally advanced GC in our hospitals from December 2013 to December 2023 were collected.There were 442 males and 210 females.The mean age was 57±12 years.All patients underwent a laparoscopic D2 radical operation for distal GC.The patients were followed up in the outpatient department and by telephone to determine their tumor recurrence,metastasis,and survival.The follow-up period ended in December 2023.Normally distributed data are expressed as the mean±SD,and normally distributed data are expressed as M(Q1,Q3)or M(range).Statistical data are expressed as absolute numbers or percentages;theχ^(2) test was used for comparisons between groups,and the Mann-Whitney U nonparametric test was used for comparisons of rank data.The life table method was used to calculate the survival rate,the Kaplan-Meier method was used to construct survival curves,the log rank test was used for survival analysis,and the Cox risk regression model was used for univariate and multifactor analysis.RESULTS The median overall survival(OS)time for the 652 patients was 81 months,with a 10-year OS rate of 46.1%.Patients with TNM stages II and III had 10-year OS rates of 59.6%and 37.5%,respectively,which were significantly different(P<0.05).Univariate analysis indicated that factors such as age,maximum tumor diameter,tumor diffe-rentiation grade(low to undifferentiated),pathological TNM stage,pathological T stage,pathological N stage(N2,N3),and postoperative chemotherapy significantly influenced the 10-year OS rate for patients with locally advanced GC following laparoscopic D2 radical resection for distal stomach cancer[hazard ratio(HR):1.45,1.64,1.45,1.64,1.37,2.05,1.30,1.68,3.08,and 0.56 with confidence intervals(CIs)of 1.15-1.84,1.32-2.03,1.05-1.77,1.62-2.59,1.05-1.61,1.17-2.42,2.15-4.41,and 0.44-0.70,respectively;P<0.05].Multifactor analysis revealed that a tumor diameter greater than 4 cm,low tumor differentiation,and pathological TNM stage III were independent risk factors for the 10-year OS rate in these patients(HR:1.48,1.44,1.81 with a 95%CI:1.19-1.84).Additionally,postoperative chemotherapy emerged as an independent protective factor for the 10-year OS rate(HR:0.57,95%CI:0.45-0.73;P<0.05).CONCLUSION A maximum tumor diameter exceeding 4 cm,low tumor differentiation,and pathological TNM stage III were identified as independent risk factors for the 10-year OS rate in patients with locally advanced GC following laparoscopic D2 radical resection for distal GC.Conversely,postoperative chemotherapy was found to be an independent protective factor for the 10-year OS rate in these patients.

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.

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.

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.

Localized Structures on Periodic Background Wave of （2＋1）-Dimensional Boiti-Leon-Pempinelli System via an Object Reduction

In this paper, we present an object reduction for nonlinear partial differential equations. As a concrete example of its applications in physical problems, this method is applied to the （2＋1）-dimensional Boiti-Leon-Pempinelli system, which has the extensive physics background, and an abundance of exact solutions is derived from some reduction equations. Based on the derived solutions, the localized structures under the periodic wave background are obtained.

A New (2+1)-Dimensional KdV Equation and Its Localized Structures

A new （2＋1）-dimensional KdV equation is constructed by using Lax pair generating technique. Exact solutions of the new equation are studied by means of the singular manifold method. Bgcklund transformation in terms of the singular manifold is obtained. And localized structures are also investigated.

LOCALIZED COHERENT STRUCTURES OF THE (2+1)-DIMENSIONAL HIGHER ORDER BROER-KAUP EQUATIONS

By using the extended homogeneous balance method, the localized coherent structures are studied. A nonlinear transformation was first established, and then the linearization form was obtained based on the extended homogeneous balance method for the higher order (2 + 1)-dimensional Broer-Kaup equations. Starting from this linearization form equation, a variable separation solution with the entrance of some arbitrary functions and some arbitrary parameters was constructed. The quite rich localized coherent structures were revealed. This method, which can be generalized to other (2 + I) -dimensional nonlinear evolution equation, is simple and powerful.

Two-dimensional atom localization via probe absorption in a four-level atomic system

We have investigated the two-dimensional （2D） atom localization via probe absorption in a coherently driven four-level atomic system by means of a radio-frequency field driving a hyperfine transition. It is found that the detecting probability and precision of 2D atom localization can be significantly improved via adjusting the system parameters. As a result, our scheme may be helpful in laser cooling or the atom nano-lithography via atom localization.

LOCAL ONE-DIMENSIONAL ASE-I SCHEME FOR 2D DIFFUSION EQUATION

A local alternating segment explicit - implicit method for the solution of 2D diffusion equations is presented in this paper .The method is unconditionally stable and has the obvious property of parallelism. Some numerical experiments show the method is not only simple but also more accurate.

Painlevé property, local and nonlocal symmetries, and symmetry reductions for a (2+1)-dimensional integrable KdV equation

The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé expansion is used to find the Schwartz form, the Bäcklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bäcklund transformation. The local point symmetries of the model constitute a centerless Kac–Moody–Virasoro algebra. The local point symmetries are used to find the related group-invariant reductions including a new Lax integrable model with a fourth-order spectral problem. The finite transformation theorem or the Lie point symmetry group is obtained by using a direct method.