{"title":"Completion of the Guo-Hierarchy Integrable Coupling with Self-Consistent Sources in a Nonlinear Wave System","authors":"Han-yu Wei, En-Gui Fan null, W. Ma","doi":"10.4208/eajam.200121.190921","DOIUrl":"https://doi.org/10.4208/eajam.200121.190921","url":null,"abstract":". Water waves are actively studied. A new method to generate new wave systems through making perturbation in matrix spectral problems for integrable couplings is presented, which is called the “completion process of integrable couplings”. As its ap-plication, we construct an integrable coupling hierarchy and show that each equation in the resulting hierarchy has a bi-Hamiltonian structure by taking use of the component-trace identity. Moreover, the self-consistent sources of integrable coupling is presented based on the theory of self-consistent sources.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47956028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Global Existence and Asymptotic Behavior in a Predator-Prey-Mutualist Model with Prey-Taxis","authors":"Qian Zhao null, Bin Liu","doi":"10.4208/eajam.220421.280921","DOIUrl":"https://doi.org/10.4208/eajam.220421.280921","url":null,"abstract":". This paper considers the global existence and boundedness of classical solutions to a predator-prey-mutualist model with prey-taxis. In addition, by constructing the Lyapunov functionals, we proved when α < ( ac / b ) · r + a / b , the positive equilibrium point is globally asymptotic stable; and when α ∈ (( ac / b ) · r + a / b , M 1 ) , the semi-trivial equilibrium point is globally asymptotic stable. Finally, we give some numerical exam-ples to validate our results.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49506165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Dynamics of Suspended Rough Platelets in Shear Flows with Different Reynolds Numbers","authors":"Kai Liu, Q. Zou, Zhipeng Xu null, Z. Tan","doi":"10.4208/eajam.300621.131221","DOIUrl":"https://doi.org/10.4208/eajam.300621.131221","url":null,"abstract":". The behaviour of platelet flows in plasma and the change of the platelet surfaces is studied by numerical simulations. In particular, the influence of the 2D platelets surface roughness and Reynolds number on the rotation of platelets is con-sidered. Reynolds numbers Re vary from 0.4 to 50 and it is noted that if Re = 50, the 2D platelets stop rotating after 90 ◦ turn. If 0.4 ≤ Re ≤ 20, the rotation period increases along with the increase of Reynolds number. The maximum angular velocity, the mini-mum angular velocity and the rotation period of platelets depends on their roughness. However, these characteristics are little affected by the roughness if the Reynolds number is close to 1. It is also worth noting that the torque of 3D platelets is greater than the torque of 2D platelets.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42108707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Simulations of Cuff-Tissue-Bone-Artery Systems for Blood Pressure Measurements","authors":"Jiacheng Xu, Dan Hu","doi":"10.4208/eajam.020322.050422","DOIUrl":"https://doi.org/10.4208/eajam.020322.050422","url":null,"abstract":"","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44999785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Lie Symmetry Analysis and Wave Propagation in Variable-Coefficient Nonlinear Physical Phenomena","authors":"Mohamed R. Ali","doi":"10.4208/eajam.100920.060121","DOIUrl":"https://doi.org/10.4208/eajam.100920.060121","url":null,"abstract":". We present Lie symmetry analysis to explore solitary wave solutions, two-soliton type solutions and three-soliton type solutions in variable-coefficient nonlinear physical phenomena. An example is a (2 + 1)-dimensional variable-coefficient Bogoyav-lensky-Konopelchenko (VCBK) equation. We compute the Lie algebra of infinitesimals of its symmetry vector fields and an optimal system of one-dimensional sub-Lie algebras of the resulting symmetries. Two stages of Lie symmetry reductions will be built to reduce the VCBK equation to nonlinear ordinary differential equations (ODEs) and new analytical solutions to those ODEs will be found by using the integration method. Some of such resulting solutions to the VCBK equation and their dynamics will be illustrated through three-dimensional plots","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70517731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Numerical Study of Time-Fractional Telegraph Equations of Transmission Line Modeling","authors":"Wang Kong, Zhongyi Huang","doi":"10.4208/eajam.070921.150222","DOIUrl":"https://doi.org/10.4208/eajam.070921.150222","url":null,"abstract":". The stability and uniqueness of the solutions of time-fractional telegraph equations arising in the transmission line modeling are proved. The corresponding initial-boundary problems are then solved by a finite difference scheme. It is shown that the scheme is unconditionally stable and convergent. Computational efficiency of the method can be enhanced by transforming it into two finite volume schemes for solving two uncoupled time-fractional convection equations. Numerical experiments validate the theoretical results and show the efficiency of this approach even for the problems the solutions which are not smooth at the initial moment.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48445631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Convex Splitting Method for Strongly Anisotropic Solid-State Dewetting Problems in Two Dimensions","authors":"Miaoyu Dai, Zhongyi Huang, Wei Zhu","doi":"10.4208/eajam.261021.120122","DOIUrl":"https://doi.org/10.4208/eajam.261021.120122","url":null,"abstract":"","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44870057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Jia, Zhiwei Yang, Xiangcheng Zheng null, Hong Wang
{"title":"Analysis and Numerical Approximation for a Nonlinear Hidden-Memory Variable-Order Fractional Stochastic Differential Equation","authors":"J. Jia, Zhiwei Yang, Xiangcheng Zheng null, Hong Wang","doi":"10.4208/eajam.311021.220222","DOIUrl":"https://doi.org/10.4208/eajam.311021.220222","url":null,"abstract":". We prove the wellposedness of a nonlinear hidden-memory variable-order fractional stochastic differential equation driven by a multiplicative white noise, in which the hidden-memory type variable order describes the memory of a fractional order. We then present a Euler-Maruyama scheme for the proposed model and prove its strong convergence rate. Numerical experiments are performed to substantiate the theoretical results.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45686387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Gui-Lin Yan, Yujiang Wu, Ai-Li Yang, Sulieman A. S. Jomah
{"title":"Two-Step Modulus-Based Synchronous Multisplitting Iteration Methods for Nonlinear Complementarity Problems","authors":"Gui-Lin Yan, Yujiang Wu, Ai-Li Yang, Sulieman A. S. Jomah","doi":"10.4208/eajam.200721.250122","DOIUrl":"https://doi.org/10.4208/eajam.200721.250122","url":null,"abstract":". Two-step modulus-based synchronous multisplitting and symmetric modulus-based synchronous multisplitting accelerated overrelaxation iteration methods are developed for solving large sparse nonlinear complementarity problems. The methods are based on the reformulation of the corresponding problem as a series of equivalent implicit fixed-point equations. This approach includes existing algorithms as special cases and present new models. The convergence of the methods is studied in the case of H + system matrices. Numerical results confirm the efficiency of the methods proposed.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":"15 9","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41290000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Deep Learning Method for Elliptic Hemivariational Inequalities","authors":"J. Huang, Chunmei Wang null, Haoqin Wang","doi":"10.4208/eajam.081121.161121","DOIUrl":"https://doi.org/10.4208/eajam.081121.161121","url":null,"abstract":". Deep learning method for solving elliptic hemivariational inequalities is con-structed. Using a variational formulation of the corresponding inequality, we reduce it to an unconstrained expectation minimization problem and solve the last one by a stochas-tic optimization algorithm. The method is applied to a frictional bilateral contact problem and to a frictionless normal compliance contact problem. Numerical experiments show that for fine meshes, the method approximates the solution with accuracy similar to the virtual element method. Besides, the use of local adaptive activation functions improves accuracy and has almost the same computational cost.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43555621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}