Pub Date : 2022-10-10DOI: 10.1515/ijnsns-2019-0200
A. Krafčík, M. Babincová, P. Babinec, I. Frollo
Abstract Magnetic carriers for guiding, delivery, and capturing of drugs to desired place attract interest in the field of smart treatment of various pathological conditions. Presented paper, therefore, deals with one such application with the theoretical model of magnetic fluid flow through vessel bifurcation with one arm treated with ferromagnetic vascular stent placed in an external originally homogeneous magnetic field. This flow was described as laminar Newtonian incompressible continuum of the magnetic many-bead system, with Reynolds number ≈ 1 $approx 1$ , using magnetic force variant of the Nernst–Planck equation coupled with the Navier–Stokes equations, solved numerically by the finite element method (FEM). This approach allowed us to quantify capturing efficiency of magnetic beads in each arm of bifurcation vessels. Results show reduction of the number of magnetic beads entering as well as leaving the arm treated with stent in comparison with the untreated one. For stented bifurcation arm, the significant amount of beads are captured to its luminal surface, which may be used for drug delivery using magnetic carriers.
{"title":"Computational study of intravenous magnetic drug targeting using implanted magnetizable stent","authors":"A. Krafčík, M. Babincová, P. Babinec, I. Frollo","doi":"10.1515/ijnsns-2019-0200","DOIUrl":"https://doi.org/10.1515/ijnsns-2019-0200","url":null,"abstract":"Abstract Magnetic carriers for guiding, delivery, and capturing of drugs to desired place attract interest in the field of smart treatment of various pathological conditions. Presented paper, therefore, deals with one such application with the theoretical model of magnetic fluid flow through vessel bifurcation with one arm treated with ferromagnetic vascular stent placed in an external originally homogeneous magnetic field. This flow was described as laminar Newtonian incompressible continuum of the magnetic many-bead system, with Reynolds number ≈ 1 $approx 1$ , using magnetic force variant of the Nernst–Planck equation coupled with the Navier–Stokes equations, solved numerically by the finite element method (FEM). This approach allowed us to quantify capturing efficiency of magnetic beads in each arm of bifurcation vessels. Results show reduction of the number of magnetic beads entering as well as leaving the arm treated with stent in comparison with the untreated one. For stented bifurcation arm, the significant amount of beads are captured to its luminal surface, which may be used for drug delivery using magnetic carriers.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":"23 1","pages":"971 - 983"},"PeriodicalIF":1.5,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46023989","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}
Pub Date : 2022-10-10DOI: 10.1515/ijnsns-2021-0340
H. Omanda, C. T. Djeumen Tchaho, D. Belobo Belobo
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.
{"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":" ","pages":""},"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}
Pub Date : 2022-10-07DOI: 10.1515/ijnsns-2021-0096
A. Koushki, Mohammad Osoolian, Seyed Jalal Sadeghi Sharif
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.
{"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":" ","pages":""},"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}
Pub Date : 2022-10-06DOI: 10.1515/ijnsns-2021-0479
C. Dineshkumar, V. Vijayakumar, R. Udhayakumar, A. Shukla, K. Nisar
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.
摘要本文讨论阶为1 < r < 2的分数阶随机Volterra-Fredholm积分微分系统的存在性和近似可控性。主要结果是应用分数阶微积分、多值映射、余弦族理论、Martelli和Dhage以及Leray-Schauder不动点技术的概念和思想得到的。我们首先强调存在性，然后证明所考虑的系统的近似可控性。此外，我们还确定了具有无限延迟的系统的近似可控性结果。最后，建立了一个应用程序来得出主要结果的理论结论。
{"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":" ","pages":""},"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}
Pub Date : 2022-10-06DOI: 10.1515/ijnsns-2021-0395
A. Z. Amin, António M. Lopes, I. Hashim
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.
{"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":" ","pages":""},"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}
Pub Date : 2022-10-06DOI: 10.1515/ijnsns-2021-0388
Emadidin Gahalla Mohmed Elmahdi, Jianfei Huang
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.
{"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":" ","pages":""},"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}
Pub Date : 2022-10-06DOI: 10.1515/ijnsns-2021-0412
K. Kavitha, V. Vijayakumar
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.
{"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":" ","pages":""},"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}
Pub Date : 2022-10-06DOI: 10.1515/ijnsns-2021-0476
S. Salman, A. Elsadany
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.
{"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":"0 1","pages":""},"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}
Pub Date : 2022-10-06DOI: 10.1515/ijnsns-2022-0112
Yanyou Qiao, Fangqi Chen, Yukun An
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.
研究一类非线性分数阶p-拉普拉斯Schr o ø $ddot{o}$ dinger耦合系统，该系统具有临界和次临界非线性项。首先，利用Nehari流形方法和Ekeland变分原理证明了系统非负基态解的存在性。此外，通过Ljusternik-Schnirelmann理论，我们将解的个数与系统中势达到最小值的集合拓扑联系起来。
{"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":" ","pages":""},"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}
Pub Date : 2022-10-06DOI: 10.1515/ijnsns-2020-0172
M. Kaplan, N. Raza
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.
{"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":"24 1","pages":"349 - 357"},"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}
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