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A Stable Time-Dependent Mesh Method for Generalized Credit Rating Migration Problem 广义信用评级迁移问题的稳定时间网格法
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2023-12-13 DOI: 10.1007/s44198-023-00157-x
Saad Sultan, Zhengce Zhang
{"title":"A Stable Time-Dependent Mesh Method for Generalized Credit Rating Migration Problem","authors":"Saad Sultan, Zhengce Zhang","doi":"10.1007/s44198-023-00157-x","DOIUrl":"https://doi.org/10.1007/s44198-023-00157-x","url":null,"abstract":"<p>The r-adaptive difference scheme is advanced in this article for solving the generalized credit rating migration model for arbitrary volatility with multiple terminal conditions. The r-adaptive moving mesh method defines the coordinate mapping from the physical to the computational domain and then uses piece-wise polynomials to approximate the physical coordinates. The central implicit semi-discretization scheme is imposed on space, and the backward Euler time marching scheme, coupled with several moving mesh partial differential equations, is used to achieve the numerical solution. The numerical operations are performed with several examples, and the obtained results are sufficiently accurate. The convergence of the proposed scheme is second-order, which is verified with the analysis. The article also investigates the stability and convergence of the adaptive mesh discretization scheme, which are not available in the literature; the convergence of the scheme is second-order in space and first-order in time.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138629299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal Control of Non-linear Volterra Integral Equations with Weakly Singular Kernels Based on Genocchi Polynomials and Collocation Method 基于 Genocchi 多项式和 Collocation 方法的具有弱奇异内核的非线性 Volterra 积分方程的优化控制
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2023-12-11 DOI: 10.1007/s44198-023-00156-y
Asiyeh Ebrahimzadeh, Elham Hashemizadeh
{"title":"Optimal Control of Non-linear Volterra Integral Equations with Weakly Singular Kernels Based on Genocchi Polynomials and Collocation Method","authors":"Asiyeh Ebrahimzadeh, Elham Hashemizadeh","doi":"10.1007/s44198-023-00156-y","DOIUrl":"https://doi.org/10.1007/s44198-023-00156-y","url":null,"abstract":"<p>We consider a problem of finding the best way to control a system, known as an optimal control problem (OCP), governed by non-linear Volterra Integral Equations with Weakly Singular kernels. The equations are based on Genocchi polynomials. Depending on the applicable properties of Genocchi polynomials, the considered OCP is converted to a non-linear programming problem (NLP). This method is speedy and provides a highly accurate solution with great precision using a small number of basis functions. The convergence analysis of the approach is also provided. The accuracy and flawless performance of the proposed technique and verification of the theory are examined with some examples.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138567032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Higher-order soliton solutions for the Sasa–Satsuma equation revisited via $$bar{partial }$$ method 通过$bar{partial }$$方法重访萨萨-萨摩方程的高阶孤子解
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2023-12-07 DOI: 10.1007/s44198-023-00160-2
YongHui Kuang, Bolin Mao, Xin Wang
{"title":"Higher-order soliton solutions for the Sasa–Satsuma equation revisited via $$bar{partial }$$ method","authors":"YongHui Kuang, Bolin Mao, Xin Wang","doi":"10.1007/s44198-023-00160-2","DOIUrl":"https://doi.org/10.1007/s44198-023-00160-2","url":null,"abstract":"<p>In optics, the Sasa–Satsuma equation can be used to model ultrashort optical pulses. In this paper higher-order soliton solutions for the Sasa–Satsuma equation with zero boundary condition at infinity are analyzed by <span>(bar{partial })</span> method. The explicit determinant form of a soliton solution which corresponds to a single <span>(p_{l})</span>-th order pole is given. Besides the interaction related to one simple pole and the other one double pole is considered.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138548156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inverse Scattering Problem for the High Order Schrödinger Operator at Fixed Angles Scattering Amplitude 固定角度散射振幅下的高阶薛定谔算子反向散射问题
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2023-12-05 DOI: 10.1007/s44198-023-00158-w
Hua Huang, Huizhen Li, Zhigang Zhou
{"title":"Inverse Scattering Problem for the High Order Schrödinger Operator at Fixed Angles Scattering Amplitude","authors":"Hua Huang, Huizhen Li, Zhigang Zhou","doi":"10.1007/s44198-023-00158-w","DOIUrl":"https://doi.org/10.1007/s44198-023-00158-w","url":null,"abstract":"<p>We consider the inverse scattering problem for the higher order Schrödinger operator <span>(H=(-Delta )^m+q(x))</span>, <span>(m=1,2, 3,ldots)</span>. We show that the scattering amplitude of <i>H</i> at fixed angles can uniquely determines the potential <i>q</i>(<i>x</i>) under certain assumptions, which extends the early results on this problem. The uniqueness of <i>q</i>(<i>x</i>) mainly depends on the construction of the Born approximation sequence and its estimation.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138560589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An RBF-FD Method for Numerical Solutions of 2D Diffusion-Wave and Diffusion Equations of Distributed Fractional Order 分布分数阶二维扩散波和扩散方程数值解的RBF-FD方法
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2023-12-04 DOI: 10.1007/s44198-023-00153-1
Fatemeh Taghipour, Ahmad Shirzadi, Mansour Safarpoor
{"title":"An RBF-FD Method for Numerical Solutions of 2D Diffusion-Wave and Diffusion Equations of Distributed Fractional Order","authors":"Fatemeh Taghipour, Ahmad Shirzadi, Mansour Safarpoor","doi":"10.1007/s44198-023-00153-1","DOIUrl":"https://doi.org/10.1007/s44198-023-00153-1","url":null,"abstract":"<p>The subject of this paper is to propose a numerical algorithm for solving 2D diffusion and diffusion-wave equations of distributed order fractional derivatives. Such equations arise in modelling complex systems and have many important applications. Existence of integral term over the order of fractional derivative causes the high complexity of these equations and so their numerical solutions needs special cares. Using Gauss quadrature approach for discretizing the integral term of fractional derivative converts the distributed equation into a multi-term fractional differential equation. Then, the time variable is discretized with a suitable finite difference approach. The resultant semi-discretized equations are fully discretized by a radial basis function-generated finite difference based method. Convergence of the method are studied numerically. Various kind of test problems are considered for a comprehensive numerical study and the results confirm the efficiency of the method.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138515177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamical Analysis of a 3D Fractional-Order Chaotic System for High-Security Communication and its Electronic Circuit Implementation 一种用于高安全性通信的三维分数阶混沌系统的动力学分析及其电子电路实现
IF 0.7 4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2023-11-20 DOI: 10.1007/s44198-023-00154-0
Girma Adam Beyene, Fahdil Rahma , Karthikeyan Rajagopal, Abdul-Basset A. Al-Hussein, Salah Boulaaras
{"title":"Dynamical Analysis of a 3D Fractional-Order Chaotic System for High-Security Communication and its Electronic Circuit Implementation","authors":"Girma Adam Beyene, Fahdil Rahma , Karthikeyan Rajagopal, Abdul-Basset A. Al-Hussein, Salah Boulaaras","doi":"10.1007/s44198-023-00154-0","DOIUrl":"https://doi.org/10.1007/s44198-023-00154-0","url":null,"abstract":"<p>This article, a 3D fractional-order chaotic system (FOCS) is designed; system holds Equilibria can take on various shapes and forms by introducing a nonlinear function and the value of its parameters. To comprehend the system’s behavior under diverse conditions and parameter values, a dynamical analysis is conducted through analytical and numerical means. This analysis employs techniques like phase portraits, Lyapunov exponents (LEs), bifurcation analysis, and Lyapunov spectra. The system demonstrates attractors that are more intricate compared to a regular chaotic system with an integer value, specifically if we set the fractional order q to 0.97. This characteristic makes it highly appropriate for developing secure communication systems. Moreover, a practical implementation has been developed using an electronic circuit to showcase its feasibility of the system. A secure communication system was built using two levels of encryption techniques. The propose sound encryption algorithm is verified through tests like histogram, correlation, and spectrogram investigation. The encryption correlation coefficient between the original signal and the encrypted one is 0.0010, this result shows a strong defences against pirate attacks.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138515171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ricci Bi-Conformal Vector Fields on Homogeneous Gödel-Type Spacetimes 齐次Gödel-Type时空上的Ricci双共形向量场
4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2023-11-13 DOI: 10.1007/s44198-023-00151-3
Shahroud Azami, Mehdi Jafari
{"title":"Ricci Bi-Conformal Vector Fields on Homogeneous Gödel-Type Spacetimes","authors":"Shahroud Azami, Mehdi Jafari","doi":"10.1007/s44198-023-00151-3","DOIUrl":"https://doi.org/10.1007/s44198-023-00151-3","url":null,"abstract":"Abstract In this paper, we consider the homogeneous Gödel-type spacetimes and we completely classify the Ricci bi-conformal vector fields on these spaces. Also, we show that all Ricci bi-conformal vector fields on homogeneous Gödel-type spacetimes are Killing vector fields and Ricci collineation vector fields.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136282502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Investigation of Dynamical Behavior of a Wing Model 机翼模型动力学行为的研究
4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2023-11-13 DOI: 10.1007/s44198-023-00152-2
Lifang Cheng, Ming Liu, Dongpo Hu, Litao Zhang
{"title":"An Investigation of Dynamical Behavior of a Wing Model","authors":"Lifang Cheng, Ming Liu, Dongpo Hu, Litao Zhang","doi":"10.1007/s44198-023-00152-2","DOIUrl":"https://doi.org/10.1007/s44198-023-00152-2","url":null,"abstract":"Abstract Bifurcations of equilibria of a wing model have been investigated in this paper. It is shown that the quintic nonlinear terms in the pitch and the plunge coordinate have affected the bifurcation structure of nontrivial equilibria in different degree. In contrast with the quintic stiffening parameter in plunge, the quintic parameter in pitch has a relatively significant effect, which will affect the number, position and stability of nontrivial equilibria. Therein two pairs of nontrivial equilibria with opposite stability coexist or disappear by two fold bifurcations. If the freestream velocity has been taken as a continuation parameter, it will affect the bifurcation structure of all the equilibria, including the trivial and the nontrivial. Wherein the equilibria vary from a trivial to two nontrivial ones by a pitchfork bifurcation. Then one of nontrivial equilibria experiences a supercritical Hopf bifurcation and the bifurcated limit cycles form an ellipsoidal structure with the limit cycles bifurcated from the trivial equilibrium.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136348575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Global Classical Limit of the (Relativistic) Vlasov–Maxwell System (相对论)Vlasov-Maxwell系统的全局经典极限
4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2023-11-13 DOI: 10.1007/s44198-023-00150-4
Donghao Li, Ling Liu, Hongwei Zhang
{"title":"On Global Classical Limit of the (Relativistic) Vlasov–Maxwell System","authors":"Donghao Li, Ling Liu, Hongwei Zhang","doi":"10.1007/s44198-023-00150-4","DOIUrl":"https://doi.org/10.1007/s44198-023-00150-4","url":null,"abstract":"Abstract It is shown that solutions of the (relativistic) Vlasov–Maxwell system converge pointwise to solutions of the Vlasov–Poisson system globally in time at the asymptotic rate of $$c^{-1},$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mi>c</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> as the light speed c tends to infinity, which extends the results of Asano and Ukai (Stud Math Appl 18:369–383, 1986), Degond (Math Methods Appl Sci 8:533–558, 1986) and Schaeffer (Commun Math Phys 104:403–421, 1986). The analysis relies on the method of Glassey and Strauss (Commun Math Phys 113:191–208, 1987) and Schaeffer (Commun Math Phys 104:403–421, 1986).","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136347305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Orbital Stability of Solitary Wave for Eckhaus–Kundu Equation Eckhaus-Kundu方程中孤波的轨道稳定性
4区 物理与天体物理
Journal of Nonlinear Mathematical Physics Pub Date : 2023-10-31 DOI: 10.1007/s44198-023-00148-y
Yuli Guo, Weiguo Zhang, Siyu Hong
{"title":"Orbital Stability of Solitary Wave for Eckhaus–Kundu Equation","authors":"Yuli Guo, Weiguo Zhang, Siyu Hong","doi":"10.1007/s44198-023-00148-y","DOIUrl":"https://doi.org/10.1007/s44198-023-00148-y","url":null,"abstract":"Abstract In this paper, the orbital stability of solitary wave for Eckhaus–Kundu equation is studied. Since the equation we studied is difficult to be expressed as a standard Hamiltonian system, the Grillakis–Shatah–Strauss theory about the orbital stability of soliton solutions for nonlinear Hamiltonian systems cannot be directly applied. By constructing three new conserved quantities and using special techniques and detailed spectral analysis, the above difficulty is overcome, then we obtain the conclusion that the solitary wave of Eckhaus–Kundu equation is orbitally stable.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135814151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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