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Hybrid solitary wave solutions of the Camassa–Holm equation Camassa-Holm方程的混合孤波解
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-10-10 DOI: 10.1515/ijnsns-2021-0340
H. Omanda, C. T. Djeumen Tchaho, D. Belobo Belobo
{"title":"Hybrid solitary wave solutions of the Camassa–Holm equation","authors":"H. Omanda, C. T. Djeumen Tchaho, D. Belobo Belobo","doi":"10.1515/ijnsns-2021-0340","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0340","url":null,"abstract":"Abstract The Camassa–Holm equation governs the dynamics of shallow water waves or in its reduced form models nonlinear dispersive waves in hyperelastic rods. By using the straightforward Bogning-Djeumen Tchaho-Kofané method, explicit expressions of many solitary wave solutions with different profiles not previously derived in the literature are constructed and classified. Geometric characterizations of the solutions in terms of three new mappings are presented. Intensive numerical simulations carried confirm the stability of the solutions even with relatively high critical velocities and reveal that solitary waves with large widths are more stable than the ones with small widths.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47499172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
An uncertainty measure based on Pearson correlation as well as a multiscale generalized Shannon-based entropy with financial market applications 基于Pearson相关和多尺度广义香农熵的不确定性测度与金融市场的应用
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-10-07 DOI: 10.1515/ijnsns-2021-0096
A. Koushki, Mohammad Osoolian, Seyed Jalal Sadeghi Sharif
{"title":"An uncertainty measure based on Pearson correlation as well as a multiscale generalized Shannon-based entropy with financial market applications","authors":"A. Koushki, Mohammad Osoolian, Seyed Jalal Sadeghi Sharif","doi":"10.1515/ijnsns-2021-0096","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0096","url":null,"abstract":"Abstract In this research, we intended to employ the Pearson correlation and a multiscale generalized Shannon-based entropy to trace the transition and type of inherent mutual information as well as correlation structures simultaneously. An optimal value for scale is found to prevent over smoothing, which leads to the removal of useful information. The lowest Singular Value Decomposition Multiscale Generalized Cumulative Residual Entropy (SVDMWGCRE), or SVD Entropy (SVDE), is obtained for periodic–chaotic series, generated by logistic map; hence, the different dynamic, correlation structures, and intrinsic mutual information have been characterized correctly. It is found out that the mutual information between emerging markets entails higher sensitivity, and moreover emerging markets have demonstrated the highest uncertainty among investigated markets. Additionally, the fractional order has synergistic effects on the enhancement of sensitivity with the multiscale feature. According to the logistic map and financial time series results, it can be inferred that the logistic map can be utilized as a financial time series. Further investigations can be performed in other fields through this financial simulation. The temporal evolutions of financial markets are also investigated. Although the results demonstrated higher noisy information for emerging markets, it was illustrated that emerging markets are getting more efficient over time. Additionally, the temporal investigations have demonstrated long-term lag and synchronous phases between developed and emerging markets. We also focused on the COVID-19 pandemic and compared the reactions of developing and emerging markets. It is ascertained that emerging markets have demonstrated higher uncertainty and overreaction to this pandemic.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42508625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Controllability discussion for fractional stochastic Volterra–Fredholm integro-differential systems of order 1 < r < 2 1 < r < 2阶的分数阶随机Volterra-Fredholm积分-微分系统的可控性讨论
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-10-06 DOI: 10.1515/ijnsns-2021-0479
C. Dineshkumar, V. Vijayakumar, R. Udhayakumar, A. Shukla, K. Nisar
{"title":"Controllability discussion for fractional stochastic Volterra–Fredholm integro-differential systems of order 1 < r < 2","authors":"C. Dineshkumar, V. Vijayakumar, R. Udhayakumar, A. Shukla, K. Nisar","doi":"10.1515/ijnsns-2021-0479","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0479","url":null,"abstract":"Abstract The main motivation of our conversation is the existence and approximate controllability for fractional stochastic Volterra–Fredholm integro-differential systems having order 1 < r < 2. The primary outcomes are obtained by applying concepts and ideas from fractional calculus, multivalued maps, the theory of cosine family, Martelli and Dhage, and Leray–Schauder fixed point techniques. We begin by emphasizing the existence, and then demonstrate the approximate controllability of the considered system. Additionally, we determine the approximate controllability outcomes for the system with infinite delay. At last, an application is established for drawing the theoretical conclusions of primary outcomes.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41978124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley–Torvik differential equation 求解非线性变阶分数阶Bagley-Torvik微分方程的Chebyshev配点法
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-10-06 DOI: 10.1515/ijnsns-2021-0395
A. Z. Amin, António M. Lopes, I. Hashim
{"title":"A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley–Torvik differential equation","authors":"A. Z. Amin, António M. Lopes, I. Hashim","doi":"10.1515/ijnsns-2021-0395","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0395","url":null,"abstract":"Abstract A numerical approach based on the shifted Chebyshev–Gauss collocation method is proposed for solving the non-linear variable-order fractional Bagley–Torvik differential equation (VO-FBTE), subject to initial and boundary conditions. The shifted fractional Chebyshev–Gauss collocation points are used as interpolation nodes, and the solution of the VO-FBTE is approximated by a truncated series of the shifted Chebyshev polynomials. The residuals are calculated at the shifted fractional Chebyshev–Gauss quadrature points. The original VO-FBTE is converted into a system of algebraic equations. The accuracy of the proposed scheme is confirmed with a set of numerical examples, and the results are compared with those obtained by other methods.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46570318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A linearized finite difference scheme for time–space fractional nonlinear diffusion-wave equations with initial singularity 具有初始奇异性的时空分数阶非线性扩散波方程的线性化有限差分格式
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-10-06 DOI: 10.1515/ijnsns-2021-0388
Emadidin Gahalla Mohmed Elmahdi, Jianfei Huang
{"title":"A linearized finite difference scheme for time–space fractional nonlinear diffusion-wave equations with initial singularity","authors":"Emadidin Gahalla Mohmed Elmahdi, Jianfei Huang","doi":"10.1515/ijnsns-2021-0388","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0388","url":null,"abstract":"Abstract This paper presents a linearized finite difference scheme for solving a kind of time-space fractional nonlinear diffusion-wave equations with initial singularity, where the Caputo fractional derivative in time and the Riesz fractional derivative in space are involved. First, the considered problem is equivalently transformed into its partial integro-differential form. Then, the fully discrete scheme is constructed by using the Crank–Nicolson technique, the L1 approximation, and the convolution quadrature formula to deal with the temporal discretizations. Meanwhile, the classical central difference formula and the fractional central difference formula are applied to approximate the second-order derivative and the Riesz fractional derivative in space, respectively. Moreover, the stability and convergence of the proposed scheme are strictly proved by using the discrete energy method. Finally, some numerical experiments are presented to illustrate the theoretical results.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46533326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ground state solutions of Schrödinger system with fractional p-Laplacian 分数p-Laplacian Schrödinger系统的基态解
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-10-06 DOI: 10.1515/ijnsns-2022-0112
Yanyou Qiao, Fangqi Chen, Yukun An
{"title":"Ground state solutions of Schrödinger system with fractional p-Laplacian","authors":"Yanyou Qiao, Fangqi Chen, Yukun An","doi":"10.1515/ijnsns-2022-0112","DOIUrl":"https://doi.org/10.1515/ijnsns-2022-0112","url":null,"abstract":"Abstract This article deals with a class of nonlinear fractional p-Laplacian Schr o ̈ $ddot{o}$ dinger coupled system with critical and subcritical nonlinear terms. Firstly, the existence of a nonnegative ground state solution of the system is proved by the Nehari manifold method and the Ekeland’s variational principle. In addition, through the Ljusternik–Schnirelmann theory, we link the number of solutions to the topology of the set in which the potentials in the system reach their minimum values.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47963111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Discussion on controllability of non-densely defined Hilfer fractional neutral differential equations with finite delay 有限时滞非稠密Hilfer分数中立型微分方程可控性的讨论
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-10-06 DOI: 10.1515/ijnsns-2021-0412
K. Kavitha, V. Vijayakumar
{"title":"Discussion on controllability of non-densely defined Hilfer fractional neutral differential equations with finite delay","authors":"K. Kavitha, V. Vijayakumar","doi":"10.1515/ijnsns-2021-0412","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0412","url":null,"abstract":"Abstract This manuscript prospects the controllability of Hilfer fractional neutral differential equations. The new results are obtained by implementing a suitable fixed point approach and the technique of measures of noncompactness and the outcomes and facts belong to fractional theory. Firstly, we focus the controllability and extend the discussion with nonlocal conditions. Finally, an interesting example is proposed to illustrate our main obtained results.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44614429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Higher order codimension bifurcations in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect 具有Allee效应的离散时间有毒-浮游植物-浮游动物模型的高阶余维分岔
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-10-06 DOI: 10.1515/ijnsns-2021-0476
S. Salman, A. Elsadany
{"title":"Higher order codimension bifurcations in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect","authors":"S. Salman, A. Elsadany","doi":"10.1515/ijnsns-2021-0476","DOIUrl":"https://doi.org/10.1515/ijnsns-2021-0476","url":null,"abstract":"Abstract In this paper, we use new methods to investigate different bifurcations of fixed points in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect. The nonstandard discretization scheme produces a discrete analog of the continuous-time toxic-phytoplankton–zooplankton model with Allee effect. The local stability for proposed system around all of its fixed points is derived. We obtain the codimension-1 conditions of various bifurcations such as period doubling and Neimark–Sacker. Moreover, the system produces codimension-2 bifurcations such as resonance 1:1, 1:2, 1:3, and 1:4. Furthermore, the system can produce very rich dynamics, such as the existence of a semi-stable limit cycle, multiple coexisting periodic orbits, and chaotic behavior. Theoretical analysis is validated by numerical methods.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41371993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Construction of complexiton-type solutions using bilinear form of Hirota-type 利用Hirota型的双线性形式构造复数型解
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-10-06 DOI: 10.1515/ijnsns-2020-0172
M. Kaplan, N. Raza
{"title":"Construction of complexiton-type solutions using bilinear form of Hirota-type","authors":"M. Kaplan, N. Raza","doi":"10.1515/ijnsns-2020-0172","DOIUrl":"https://doi.org/10.1515/ijnsns-2020-0172","url":null,"abstract":"Abstract In this paper, based on the Hirota bilinear form and the extended transformed rational function method, complexiton solutions have been found of the Hirota–Satsuma–Ito (HSI) equation and generalized Calogero–Bogoyavlenskii–Schiff equation through a direct symbolic computation with Maple. This method is the improved form of the transformed rational function method. The obtained complexiton solutions, includes trigonometric and hyperbolic trigonometric solutions, have verified utilizing Hirota bilinear forms. Also, a graphical representation of the obtained solutions is given.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45028408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Lie symmetry analysis for two-phase flow with mass transfer 具有传质的两相流的李对称性分析
IF 1.5 4区 工程技术
International Journal of Nonlinear Sciences and Numerical Simulation Pub Date : 2022-10-06 DOI: 10.1515/ijnsns-2022-0126
A. Paliathanasis
{"title":"Lie symmetry analysis for two-phase flow with mass transfer","authors":"A. Paliathanasis","doi":"10.1515/ijnsns-2022-0126","DOIUrl":"https://doi.org/10.1515/ijnsns-2022-0126","url":null,"abstract":"Abstract We perform a complete symmetry classification for the hyperbolic system of partial differential equations, which describes a drift-flux two-phase flow in a one-dimensional pipe, with a mass-transfer term between the two different phases of the fluid. In addition, we consider the polytropic equation of states parameter and gravitational forces. For general values of the polytropic indices, we find that the fluid equations are invariant under the elements of a three-dimensional Lie algebra. However, additional Lie point symmetries follow for specific values of the polytropic indices. The one-dimensional systems are investigated in each case of the classification scheme, and the similarity transformations are calculated in order to reduce the fluid equations into a system of ordinary differential equations. Exact solutions are derived, while the reduced systems are studied numerically.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48517721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","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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