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.

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.

不同强度运动干预2型糖尿病大鼠骨骼肌羧酸酯酶1及炎症因子的变化

背景:羧酸酯酶1及炎症因子在调节脂质代谢以及葡萄糖稳态方面起着至关重要的作用,然而有关不同强度运动干预对2型糖尿病大鼠骨骼肌羧酸酯酶1及炎症因子的影响尚待揭示。目的:探究不同强度运动干预对2型糖尿病大鼠骨骼肌羧酸酯酶1及炎症因子的影响。方法:取32只8周龄雄性SD大鼠,适应性喂养1周后随机分为正常对照组(n=12)和造模组(n=20),造模组大鼠利用高脂膳食和一次性注射链脲佐菌素制备2型糖尿病模型,建模成功后随机分为糖尿病对照组(n=6)、中等强度运动组(n=6)和高强度间歇运动组(n=6),后2组适应性跑台运动5 d后分别进行对应强度的跑台运动,每天1次,每次50 min,每周训练5 d。连续运动6周后,检测大鼠血糖与血脂相关指标,苏木精-伊红染色观察骨骼肌组织形态学变化,qRT-PCR检测骨骼肌羧酸酯酶1与炎症因子的mRNA表达,Western-blotting及免疫荧光染色检测骨骼肌中羧酸酯酶1与炎症因子的蛋白表达。结果与结论:①与正常对照组相比,糖尿病对照组大鼠空腹血糖、三酰甘油、低密度脂蛋白胆固醇、胰岛素抵抗指数均升高(P<0.05),胰岛素活性降低(P<0.05),骨骼肌中的羧酸酯酶1、NEK7、白细胞介素18的mRNA与蛋白表达均升高(P<0.05)。②与糖尿病对照组相比,中等强度运动组和高强度间歇运动组大鼠空腹血糖、三酰甘油、低密度脂蛋白胆固醇、胰岛素抵抗指数均降低(P<0.05),胰岛素活性升高(P<0.05);中等强度运动组大鼠骨骼肌中的NEK7 mRNA表达降低(P<0.01),羧酸酯酶1、NEK7、白细胞介素18蛋白表达降低(P<0.05);高强度间歇运动组大鼠骨骼肌中的羧酸酯酶1、NEK7、NLRP3、白细胞介素18 mRNA表达降低(P<0.05),羧酸酯酶1、白细胞介素18蛋白表达降低(P<0.05)。③苏木精-伊红染色显示,相较于糖尿病对照组,中等强度运动组大鼠肌纤维间隙变小,内部空洞减少,细胞结构趋于完整;高强度间歇运动组大鼠肌细胞排列松散,组织形态不规则,肌纤维内部空洞较多。④结果表明,中等强度运动和高强度间歇运动均可降低2型糖尿病大鼠的血糖、血脂、胰岛素抵抗与骨骼肌羧酸酯酶1水平,中等强度运动可明显降低骨骼肌NEK7表达,高强度间歇运动可降低骨骼肌白细胞介素18表达,并且羧酸酯酶1与NEK7、白细胞介素18关系密切。

miR-192-5p靶向CKIP-1促进骨质疏松患者骨髓间充质干细胞成骨分化

背景:酪蛋白激酶2结合蛋白1(casein kinase 2-interaction protein-1,CKIP-1)是一种重要的骨形成负调控基因,其敲除鼠骨质显著增强、骨形成和骨密度也显著提高。而miRNA作为较早发现的小分子调控物,对大多数编码基因具有调控作用,在成骨分化中发挥重要作用。目的:探讨miRNA/CKIP-1对骨质疏松患者骨髓间充质干细胞成骨分化的影响及其分子机制。方法:采用miRNA-Seq技术检测2022年3-6月在开封市中心医院骨外科就诊32例骨质疏松患者及同期体检中心健康人群骨髓间充质干细胞中miRNA的变化情况;利用Targetscan网站预测靶向调控CKIP-1的miRNA,利用荧光素酶报告基因实验检测miRNA与CKIP-1启动子区DNA的结合;在骨髓间充质干细胞中转染miR-192-5p类似物(miR-192-5p mimics)/阴性对照(NC mimics)或miR-192-5p抑制剂(miR-192-5p inhibitor)/阴性对照(NC inhibitor),成骨诱导后第7,14天,通过实时荧光定量PCR技术及茜素红染色检测成骨标志基因Runt相关转录因子2(Runx2)、骨钙素、抗骨桥蛋白、骨唾液蛋白及CKIP-1的表达水平和骨髓间充质干细胞向成骨细胞分化的情况;采用蛋白质免疫印迹实验及茜素红染色检测miR-192-5p/CKIP-1/轴对细胞成骨分化的的调控作用。结果与结论:与健康组相比,骨质疏松组有16个miRNA表达明显升高,53个miRNA表达明显降低(P<0.05);利用Targetscan网站预测,并通过荧光素酶报告基因实验验证,发现miR-192-5p与CKIP-1有互补的核苷酸序列(P<0.05);过表达miR-192-5p,Runx2、骨钙素、骨桥素和骨唾液蛋白的表达水平显著升高(P<0.05),抑制miR-192-5p,Runx2、骨钙素、骨桥素和骨唾液蛋白的表达水平显著降低(P<0.05),而沉默CKIP-1的表达后,Runx2、骨钙素及骨桥素的蛋白水平增加(P<0.05),逆转了敲低miR-192-5p对细胞成骨分化的抑制作用。上述结果证实,miR-192-5p在骨质疏松症中表达降低;miR-192-5p通过靶向抑制CKIP-1的表达,促进骨髓间充质干细胞成骨分化。

SphK1/S1P/S1PR2信号通路促进肌生成:运动改善骨骼肌健康的新视角

背景:近年来,运动改善骨骼肌的健康已成为学者们关注的一个重要研究内容,适宜的运动对骨骼肌具有积极的作用,其中在运动激活鞘氨醇激酶1(sphingosine kinase1,SphK1)/鞘氨醇-1-磷酸(sphingosine-1-phosphate,S1P)/鞘氨醇-1-磷酸受体2(sphingosine-1-phosphate receptor2,S1PR2)信号通路如何改善骨骼肌的健康,正受到科研人员的重视。目的:研究运动经SphK1/S1P/S1PR2信号通路如何改善骨骼肌的健康,探索治疗相关肌肉疾病的新方法,以改善人的骨骼肌健康。方法:检索Web of Science、PubMed、中国知网、万方和维普数据库从建库至今与文章主题相关的文献,以“signaling pathway,SphK1,S1P,S1PR2,skeletal muscle,satellite cell,myogenesis,exercise”为英文检索词,以“信号通路,SphK1,S1P,S1PR2,骨骼肌,卫星细胞,肌生成,运动”为中文检索词,最终纳入69篇文献进行分析。结果与结论:①SphK1/S1P/S1PR2信号通路是一个复杂的调控网络,通过SphK1催化产生的S1P,与S1PR2等受体的相互作用,触发下游信号转导过程,进而调控细胞、组织、器官和系统的多种生物学功能。②SphK1/S1P/S1PR2信号通路能调控卫星细胞增殖和成肌细胞分化,改善肌生成。③文章通过文献资料调研法分析了SphK1/S1P/S1PR2信号通路的生理基础以及运动对其影响的可能性。急性有氧运动可提高骨骼肌中SphK1的表达,人体和动物研究中已证实急性和长期运动均可提高骨骼肌中S1P水平,另外研究表明长期抗阻运动可提高S1PR2在骨骼肌中的表达,部分实验结果表明急性和长期运动对肌肉或者血液中S1P水平无显著影响,出现不同结果的原因可能是选择的研究对象、方式、强度及频率不同,而具体机制尚不明确。④研究认为,运动能够促进SphK1/S1P/S1PR2信号通路在骨骼肌中的表达,调控下游相关信号通路,并且针对这一信号通路的研究可能为骨骼肌疾病的治疗提供新的策略和方法,从而改善骨骼肌健康。⑤未来应深化对SphK1/S1P/S1PR2信号通路与骨骼肌健康关联的研究,进一步揭示其与卫星细胞、成肌细胞的调控关系及与上下游通路的相互作用,挖掘其临床应用价值,制定康复方案时考虑该通路变化,探索不同运动对该通路的影响机制,并将其作为潜在治疗靶点,结合人体肌肉模型提升研究深度和准确性。

骨疏康干预破骨细胞:激活核因子E2相关因子2调控c-Fos/NFATc1通路

背景:已有研究表明,骨疏康通过调节核苷酸、氨基酸代谢和免疫机制影响骨骼代谢,目前骨疏康治疗骨质疏松症的机制研究主要聚焦于调控成骨细胞,对破骨细胞的关注较少。目的:以RAW 264.7细胞为实验对象,从破骨细胞角度探讨骨疏康治疗骨质疏松症的机制。方法:取8周龄雌性SD大鼠24只,采用随机数字表法分为4组(n=6),3个实验组分别灌胃给予1,2,4 g/kg的骨疏康药液(2次/d),对照组灌胃给予等量蒸馏水(2次/d),连续灌胃7 d后抽取大鼠主动脉血,离心收集血清,同组血清合并,获得低、中、高浓度的骨疏康含药血清及正常血清,进行后续实验。①将RAW 264.7细胞分6组培养:对照组加入正常血清,低、中、高浓度组分别加入低、中、高浓度的骨疏康含药血清,Nrf2抑制剂组加入核因子E2相关因子2(nuclear factor erythroid 2-related factor 2,Nrf2)抑制剂ML385,Nrf2激活剂组加入Nrf2激活剂t-BHQ,采用CCK8法检测细胞相对活性。②将第3代RAW 264.7细胞分5组培养:空白对照组加入正常血清,破骨组加入核因子κB受体活化因子配体(receptor activator of nuclear factorκB ligand,RANKL),低、中、高浓度组在加入RANKL的基础上分别加入低、中、高浓度的骨疏康含药血清,培养5 d后进行抗酒石酸酸性磷酸染色。③将RAW 264.7细胞分5组培养:空白对照组加入正常血清,破骨组加入正常血清与RANKL,高浓度+破骨组加入RANKL+高浓度骨疏康含药血清,破骨+Nrf2激动剂组加入RANKL+t-BHQ,高浓度+破骨+Nrf2抑制剂组加入RANKL+高浓度骨疏康含药血清+ML385,培养5 d后进行Western Blot与活性氧含量检测。结果与结论:①CCK8检测结果显示,骨疏康含药血清及Nrf2抑制剂、激动剂对RAW 264.7细胞活力无明显影响;②抗酒石酸酸性磷酸染色结果显示,骨疏康含药血清呈浓度依赖性抑制破骨细胞的分化;③Western Blot与活性氧含量检测结果显示,与空白对照组比较,破骨组Nrf2蛋白表达降低(P<0.05),c-Fos、NFATc1蛋白表达与活性氧含量升高(P<0.05);与破骨组比较,高浓度+破骨组、破骨+Nrf2激动剂组、高浓度+破骨+Nrf2抑制剂组Nrf2蛋白表达升高、活性氧含量降低(P<0.05),高浓度+破骨组、破骨+Nrf2激动剂组c-Fos、NFATc1蛋白表达降低(P<0.05);与高浓度+破骨组比较,高浓度+破骨+Nrf2抑制剂组Nrf2蛋白表达降低(P<0.05),活性氧含量升高(P<0.05);④结果表明,骨疏康通过激活Nrf2减少活性氧生成,进而抑制下游c-Fos/NFATc1通路表达和破骨细胞分化。

Characteristic changes in astrocyte properties during astrocyte-to-neuron conversion induced by NeuroD1/Ascl1/Dlx2

Direct in vivo conversion of astrocytes into functional new neurons induced by neural transcription factors has been recognized as a potential new therapeutic intervention for neural injury and degenerative disorders. However, a few recent studies have claimed that neural transcription factors cannot convert astrocytes into neurons, attributing the converted neurons to pre-existing neurons mis-expressing transgenes. In this study, we overexpressed three distinct neural transcription factors––NeuroD1, Ascl1, and Dlx2––in reactive astrocytes in mouse cortices subjected to stab injury, resulting in a series of significant changes in astrocyte properties. Initially, the three neural transcription factors were exclusively expressed in the nuclei of astrocytes. Over time, however, these astrocytes gradually adopted neuronal morphology, and the neural transcription factors was gradually observed in the nuclei of neuron-like cells instead of astrocytes. Furthermore,we noted that transcription factor-infected astrocytes showed a progressive decrease in the expression of astrocytic markers AQP4(astrocyte endfeet signal), CX43(gap junction signal), and S100β. Importantly, none of these changes could be attributed to transgene leakage into preexisting neurons. Therefore, our findings suggest that neural transcription factors such as NeuroD1, Ascl1, and Dlx2 can effectively convert reactive astrocytes into neurons in the adult mammalian brain.

P2Y1 receptor in Alzheimer’s disease

Alzheimer’s disease is the most frequent form of dementia characterized by the deposition of amyloid-beta plaques and neurofibrillary tangles consisting of hyperphosphorylated tau.Targeting amyloid-beta plaques has been a primary direction for developing Alzheimer’s disease treatments in the last decades.However,existing drugs targeting amyloid-beta plaques have not fully yielded the expected results in the clinic,necessitating the exploration of alternative therapeutic strategies.Increasing evidence unravels that astrocyte morphology and function alter in the brain of Alzheimer’s disease patients,with dysregulated astrocytic purinergic receptors,particularly the P2Y1 receptor,all of which constitute the pathophysiology of Alzheimer’s disease.These receptors are not only crucial for maintaining normal astrocyte function but are also highly implicated in neuroinflammation in Alzheimer’s disease.This review delves into recent insights into the association between P2Y1 receptor and Alzheimer’s disease to underscore the potential neuroprotective role of P2Y1 receptor in Alzheimer’s disease by mitigating neuroinflammation,thus offering promising avenues for developing drugs for Alzheimer’s disease and potentially contributing to the development of more effective treatments.

AAV2-PDE6B restores retinal structure and function in the retinal degeneration 10 mouse model of retinitis pigmentosa by promoting phototransduction and inhibiting apoptosis

Retinitis pigmentosa is a group of inherited diseases that lead to retinal degeneration and photoreceptor cell death.However,there is no effective treatment for retinitis pigmentosa caused by PDE6B mutation.Adeno-associated virus(AAV)-mediated gene therapy is a promising strategy for treating retinitis pigmentosa.The aim of this study was to explore the molecular mechanisms by which AAV2-PDE6B rescues retinal function.To do this,we injected retinal degeneration 10(rd10)mice subretinally with AAV2-PDE6B and assessed the therapeutic effects on retinal function and structure using dark-and light-adapted electroretinogram,optical coherence tomography,and immunofluorescence.Data-independent acquisition-mass spectrometry-based proteomic analysis was conducted to investigate protein expression levels and pathway enrichment,and the results from this analysis were verified by real-time polymerase chain reaction and western blotting.AAV2-PDE6B injection significantly upregulated PDE6βexpression,preserved electroretinogram responses,and preserved outer nuclear layer thickness in rd10 mice.Differentially expressed proteins between wild-type and rd10 mice were closely related to visual perception,and treating rd10 mice with AAV2-PDE6B restored differentially expressed protein expression to levels similar to those seen in wild-type mice.Kyoto Encyclopedia of Genes and Genome analysis showed that the differentially expressed proteins whose expression was most significantly altered by AAV2-PDE6B injection were enriched in phototransduction pathways.Furthermore,the phototransductionrelated proteins Pde6α,Rom1,Rho,Aldh1a1,and Rbp1 exhibited opposite expression patterns in rd10 mice with or without AAV2-PDE6B treatment.Finally,Bax/Bcl-2,p-ERK/ERK,and p-c-Fos/c-Fos expression levels decreased in rd10 mice following AAV2-PDE6B treatment.Our data suggest that AAV2-PDE6B-mediated gene therapy promotes phototransduction and inhibits apoptosis by inhibiting the ERK signaling pathway and upregulating Bcl-2/Bax expression in retinitis pigmentosa.

Recombinant chitinase-3-like protein 1 alleviates learning and memory impairments via M2 microglia polarization in postoperative cognitive dysfunction mice

Postoperative cognitive dysfunction is a seve re complication of the central nervous system that occurs after anesthesia and surgery,and has received attention for its high incidence and effect on the quality of life of patients.To date,there are no viable treatment options for postoperative cognitive dysfunction.The identification of postoperative cognitive dysfunction hub genes could provide new research directions and therapeutic targets for future research.To identify the signaling mechanisms contributing to postoperative cognitive dysfunction,we first conducted Gene Ontology and Kyoto Encyclopedia of Genes and Genomes pathway enrichment analyses of the Gene Expression Omnibus GSE95426 dataset,which consists of mRNAs and long non-coding RNAs differentially expressed in mouse hippocampus3 days after tibial fracture.The dataset was enriched in genes associated with the biological process"regulation of immune cells,"of which Chill was identified as a hub gene.Therefore,we investigated the contribution of chitinase-3-like protein 1 protein expression changes to postoperative cognitive dysfunction in the mouse model of tibial fractu re surgery.Mice were intraperitoneally injected with vehicle or recombinant chitinase-3-like protein 124 hours post-surgery,and the injection groups were compared with untreated control mice for learning and memory capacities using the Y-maze and fear conditioning tests.In addition,protein expression levels of proinflammatory factors(interleukin-1βand inducible nitric oxide synthase),M2-type macrophage markers(CD206 and arginase-1),and cognition-related proteins(brain-derived neurotropic factor and phosphorylated NMDA receptor subunit NR2B)were measured in hippocampus by western blotting.Treatment with recombinant chitinase-3-like protein 1 prevented surgery-induced cognitive impairment,downregulated interleukin-1βand nducible nitric oxide synthase expression,and upregulated CD206,arginase-1,pNR2B,and brain-derived neurotropic factor expression compared with vehicle treatment.Intraperitoneal administration of the specific ERK inhibitor PD98059 diminished the effects of recombinant chitinase-3-like protein 1.Collectively,our findings suggest that recombinant chitinase-3-like protein 1 ameliorates surgery-induced cognitive decline by attenuating neuroinflammation via M2 microglial polarization in the hippocampus.Therefore,recombinant chitinase-3-like protein1 may have therapeutic potential fo r postoperative cognitive dysfunction.

Drosophila models used to simulate human ATP1A1 gene mutations that cause Charcot-Marie-Tooth type 2 disease and refractory seizures

Certain amino acids changes in the human Na^(+)/K^(+)-ATPase pump,ATPase Na^(+)/K^(+)transporting subunit alpha 1(ATP1A1),cause Charcot-Marie-Tooth disease type 2(CMT2)disease and refractory seizures.To develop in vivo models to study the role of Na^(+)/K^(+)-ATPase in these diseases,we modified the Drosophila gene homolog,Atpα,to mimic the human ATP1A1 gene mutations that cause CMT2.Mutations located within the helical linker region of human ATP1A1(I592T,A597T,P600T,and D601F)were simultaneously introduced into endogenous Drosophila Atpαby CRISPR/Cas9-mediated genome editing,generating the Atpα^(TTTF)model.In addition,the same strategy was used to generate the corresponding single point mutations in flies(Atpα^(I571T),Atpα^(A576T),Atpα^(P579T),and Atpα^(D580F)).Moreover,a deletion mutation(Atpα^(mut))that causes premature termination of translation was generated as a positive control.Of these alleles,we found two that could be maintained as homozygotes(Atpα^(I571T)and Atpα^(P579T)).Three alleles(Atpα^(A576T),Atpα^(P579)and Atpα^(D580F))can form heterozygotes with the Atpαmut allele.We found that the Atpαallele carrying these CMT2-associated mutations showed differential phenotypes in Drosophila.Flies heterozygous for Atpα^(TTTF)mutations have motor performance defects,a reduced lifespan,seizures,and an abnormal neuronal morphology.These Drosophila models will provide a new platform for studying the function and regulation of the sodium-potassium pump.

Prolonged intermittent theta burst stimulation restores the balance between A_(2A)R-and A_(1)R-mediated adenosine signaling in the 6-hydroxidopamine model of Parkinson's disease

An imbalance in adenosine-mediated signaling,particularly the increased A_(2A)R-mediated signaling,plays a role in the pathogenesis of Parkinson's disease.Existing therapeutic approaches fail to alter disease progression,demonstrating the need for novel approaches in PD.Repetitive transcranial magnetic stimulation is a non-invasive approach that has been shown to improve motor and non-motor symptoms of Parkinson's disease.However,the underlying mechanisms of the beneficial effects of repetitive transcranial magnetic stimulation remain unknown.The purpose of this study is to investigate the extent to which the beneficial effects of prolonged intermittent theta burst stimulation in the 6-hydroxydopamine model of experimental parkinsonism are based on modulation of adenosine-mediated signaling.Animals with unilateral 6-hydroxydopamine lesions underwent intermittent theta burst stimulation for 3 weeks and were tested for motor skills using the Rotarod test.Immunoblot,quantitative reverse transcription polymerase chain reaction,immunohistochemistry,and biochemical analysis of components of adenosine-mediated signaling were performed on the synaptosomal fraction of the lesioned caudate putamen.Prolonged intermittent theta burst stimulation improved motor symptoms in 6-hydroxydopamine-lesioned animals.A 6-hydroxydopamine lesion resulted in progressive loss of dopaminergic neurons in the caudate putamen.Treatment with intermittent theta burst stimulation began 7 days after the lesion,coinciding with the onset of motor symptoms.After treatment with prolonged intermittent theta burst stimulation,complete motor recovery was observed.This improvement was accompanied by downregulation of the e N/CD73-A_(2A)R pathway and a return to physiological levels of A_(1)R-adenosine deaminase 1 after 3 weeks of intermittent theta burst stimulation.Our results demonstrated that 6-hydroxydopamine-induced degeneration reduced the expression of A_(1)R and elevated the expression of A_(2A)R.Intermittent theta burst stimulation reversed these effects by restoring the abundances of A_(1)R and A_(2A)R to control levels.The shift in ARs expression likely restored the balance between dopamine-adenosine signaling,ultimately leading to the recovery of motor control.

Abundant invariant solutions of extended(3+1)-dimensional KP-Boussinesq equation

Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generators.By selecting suitable arbitrary functions in the similarity reduction solutions,we obtain abundant invariant solutions,including the trigonometric solution,the kink-lump interaction solution,the interaction solution between lump wave and triangular periodic wave,the two-kink solution,the lump solution,the interaction between a lump and two-kink and the periodic lump solution in different planes.These exact solutions are also given graphically to show the detailed structures of this high dimensional integrable system.

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.

New Exact Solutions for （2＋1）-Dimensional Breaking Soliton Equation

New exact solutions in terms of the Jacobi elliptic functions are obtained to the (2+1)-dimensional breakingsoliton equation by means of the modified mapping method. Limit cases are studied, and new solitary wave solutionsand triangular periodic wave solutions are obtained.

A General Mapping Approach and New Travelling Wave Solutions to（2＋1）-Dimensional Boussinesq Equation

A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.

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.

Study of （2＋1）-Dimensional Higher-Order Broer-Kaup System

Painleve property and infinite symmetries of the （2＋1）-dimensional higher-order Broer-Kaup （HBK） system are studied in this paper. Using the modified direct method, we derive the theorem of general symmetry gro.ups to （2＋1）-dimensional HBK system. Based on our theorem, some new forms of solutions are obtained. We also find infinite number of conservation laws of the （2＋1）-dimensional HBK system.