Pub Date : 2023-09-27DOI: 10.1007/s44198-023-00143-3
Elyas Shivanian
Abstract This study focuses on investigating the existence and uniqueness of a solution to a specific type of high-order nonlinear fractional differential equations that include the Rieman-Liouville fractional derivative. The boundary condition is of integral type, which involves both the starting and ending points of the domain. Initially, the unique exact solution is derived using Green’s function for the linear fractional differential equation. Subsequently, the Banach contraction mapping theorem is employed to establish the main result for the general nonlinear source term case. Moreover, an illustrative example is presented to demonstrate the legitimacy and applicability of our main result.
{"title":"On the Existence and Uniqueness of the Solution of a Nonlinear Fractional Differential Equation with Integral Boundary Condition","authors":"Elyas Shivanian","doi":"10.1007/s44198-023-00143-3","DOIUrl":"https://doi.org/10.1007/s44198-023-00143-3","url":null,"abstract":"Abstract This study focuses on investigating the existence and uniqueness of a solution to a specific type of high-order nonlinear fractional differential equations that include the Rieman-Liouville fractional derivative. The boundary condition is of integral type, which involves both the starting and ending points of the domain. Initially, the unique exact solution is derived using Green’s function for the linear fractional differential equation. Subsequently, the Banach contraction mapping theorem is employed to establish the main result for the general nonlinear source term case. Moreover, an illustrative example is presented to demonstrate the legitimacy and applicability of our main result.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135536532","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}
Pub Date : 2023-09-27DOI: 10.1007/s44198-023-00141-5
Zhenshu Wen
Abstract We prove that limit wave speed is decreasing for the pgKdV equation with nonlinear terms of arbitrary higher degree in a numerical way. Our results provide the complete answer to the open question suggested by Yan et al. (Math Model Anal 19:537–555, 2014).
{"title":"On the Monotonicity of Limit Wave Speed of the pgKdV Equation with Nonlinear Terms of Arbitrary Higher Degree","authors":"Zhenshu Wen","doi":"10.1007/s44198-023-00141-5","DOIUrl":"https://doi.org/10.1007/s44198-023-00141-5","url":null,"abstract":"Abstract We prove that limit wave speed is decreasing for the pgKdV equation with nonlinear terms of arbitrary higher degree in a numerical way. Our results provide the complete answer to the open question suggested by Yan et al. (Math Model Anal 19:537–555, 2014).","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135537088","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}
Pub Date : 2023-09-26DOI: 10.1007/s44198-023-00140-6
Baiying He, Shiyuan Liu, Siyu Gao
Abstract Based on the symplectic Lie algebra $$mathfrak {sp}(4)$$ sp(4) , we obtain two integrable hierarchies of $$mathfrak {sp}(4)$$ sp(4) , and by using the trace identity, we give their Hamiltonian structures. Then, we use $$2times 2$$ 2×2 Kronecker product, and construct integrable coupling systems of one soliton equation. Next, we consider two bases of Lie algebra $$mathfrak {so}(5)$$ so(5) , and we get the corresponding two integrable hierarchies. Finally, we discuss the relation between the integrable hierarchies of two different bases associated with Lie algebra $$mathfrak {so}(5)$$ so(5) .
{"title":"Some Soliton Hierarchies Associated with Lie Algebras $$mathfrak {sp}(4)$$ and $$mathfrak {so}(5)$$","authors":"Baiying He, Shiyuan Liu, Siyu Gao","doi":"10.1007/s44198-023-00140-6","DOIUrl":"https://doi.org/10.1007/s44198-023-00140-6","url":null,"abstract":"Abstract Based on the symplectic Lie algebra $$mathfrak {sp}(4)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>sp</mml:mi> <mml:mo>(</mml:mo> <mml:mn>4</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , we obtain two integrable hierarchies of $$mathfrak {sp}(4)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>sp</mml:mi> <mml:mo>(</mml:mo> <mml:mn>4</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , and by using the trace identity, we give their Hamiltonian structures. Then, we use $$2times 2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> Kronecker product, and construct integrable coupling systems of one soliton equation. Next, we consider two bases of Lie algebra $$mathfrak {so}(5)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>so</mml:mi> <mml:mo>(</mml:mo> <mml:mn>5</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , and we get the corresponding two integrable hierarchies. Finally, we discuss the relation between the integrable hierarchies of two different bases associated with Lie algebra $$mathfrak {so}(5)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>so</mml:mi> <mml:mo>(</mml:mo> <mml:mn>5</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> .","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134961124","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}
摘要本文研究了$$begin{aligned} f^{n}(z)+Q(z,f)=beta _{1}e^{alpha _{1}z}+beta _{2}e^{alpha _{2}z}+cdots +beta _{s}e^{alpha _{s}z} end{aligned}$$ f n (z) + Q (z, f) = β 1 e α 1 z + β 2 e α 2 z +⋯⋯+ β s e α s z和$$begin{aligned} f^{n}(z)f^{(k)}(z)+L_d(z,f)=sum ^{s}_{i=1}p_i(z)e^{alpha _i{(z)}}, end{aligned}$$ f n (z) f (k) (z) + L d (z, f) =∑i = 1 s p i (z) e α i (z)，其中n, s为正整数，$$nge s+2,$$ n≥s + 2, Q (z)，F)是F中阶为d的微分-差分多项式。
Pub Date : 2023-09-20DOI: 10.1007/s44198-023-00135-3
Akbar Dehghan Nezhad, Mina Moghaddam Zeabadi
Abstract We define a Lie algebroid structure for a class of vector bundles of rank k over a k -dimensional smooth manifold W , which are isomorphic to the tangent bundle TW . We construct an exciting example of these types of vector bundles. This example is constructed based on partial Caputo fractional derivatives. We call this vector bundle a fractional vector bundle and denote it by $${mathscr {F}}^{nu } {mathscr {W}}$$ FνW .
摘要定义了k维光滑流形W上一类秩k的向量束的李代数结构，它们与切束TW同构。我们构造了这类向量束的一个令人兴奋的例子。这个例子是基于偏卡普托分数阶导数构造的。我们称这个向量束为分数向量束，用$${mathscr {F}}^{nu } {mathscr {W}}$$ F ν W表示。
{"title":"A Lie Algebroid Structure for Vector Bundles of Finite Rank Isomorphic to Tangent Bundle of Their Base Space","authors":"Akbar Dehghan Nezhad, Mina Moghaddam Zeabadi","doi":"10.1007/s44198-023-00135-3","DOIUrl":"https://doi.org/10.1007/s44198-023-00135-3","url":null,"abstract":"Abstract We define a Lie algebroid structure for a class of vector bundles of rank k over a k -dimensional smooth manifold W , which are isomorphic to the tangent bundle TW . We construct an exciting example of these types of vector bundles. This example is constructed based on partial Caputo fractional derivatives. We call this vector bundle a fractional vector bundle and denote it by $${mathscr {F}}^{nu } {mathscr {W}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> <mml:mi>ν</mml:mi> </mml:msup> <mml:mi>W</mml:mi> </mml:mrow> </mml:math> .","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"172 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136308354","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}
Pub Date : 2023-09-13DOI: 10.1007/s44198-023-00139-z
Ramin Kazemi, Mohammad Qasem Vahidi-Asl
Abstract The spread of COVID-19 can be greatly influenced by human mobility. However, implementing control measures based on restrictions can be costly. That is why it is crucial to develop a quarantine strategy that can minimize the spread of the disease while also reducing costs. This article focuses on determining the percolation threshold of COVID-19 in Tehran province using a square lattice and two types of city connections. The study identifies the number of roads that need to be closed and the cities that should be quarantined. Monte Carlo simulations using the Newman and Ziff and Union-Find algorithms were conducted through the $$text {SEAIRD}$$ SEAIRD model to assess the effectiveness of the proposed measures. The results showed a possible reduction of 81 $$%$$ % in disease spread. This approach can be used in other regions to assist in the development of public health policies.
COVID-19的传播受人员流动的影响很大。然而，基于限制实施控制措施可能代价高昂。这就是为什么制定一种既能最大限度地减少疾病传播又能降低成本的隔离战略至关重要。本文的重点是使用方形网格和两种类型的城市连接来确定德黑兰省COVID-19的渗透阈值。该研究确定了需要关闭的道路数量和应该隔离的城市。通过$$text {SEAIRD}$$ SEAIRD模型，使用Newman和Ziff以及Union-Find算法进行蒙特卡罗模拟，以评估所提出措施的有效性。结果显示可能减少81 $$%$$ % in disease spread. This approach can be used in other regions to assist in the development of public health policies.
{"title":"Percolation Analysis of COVID-19 Epidemic","authors":"Ramin Kazemi, Mohammad Qasem Vahidi-Asl","doi":"10.1007/s44198-023-00139-z","DOIUrl":"https://doi.org/10.1007/s44198-023-00139-z","url":null,"abstract":"Abstract The spread of COVID-19 can be greatly influenced by human mobility. However, implementing control measures based on restrictions can be costly. That is why it is crucial to develop a quarantine strategy that can minimize the spread of the disease while also reducing costs. This article focuses on determining the percolation threshold of COVID-19 in Tehran province using a square lattice and two types of city connections. The study identifies the number of roads that need to be closed and the cities that should be quarantined. Monte Carlo simulations using the Newman and Ziff and Union-Find algorithms were conducted through the $$text {SEAIRD}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mtext>SEAIRD</mml:mtext> </mml:math> model to assess the effectiveness of the proposed measures. The results showed a possible reduction of 81 $$%$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>%</mml:mo> </mml:math> in disease spread. This approach can be used in other regions to assist in the development of public health policies.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135741872","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}
Pub Date : 2023-09-05DOI: 10.1007/s44198-023-00137-1
Peijun Zhang, Weipeng Hu, Zhen Wang, Zhijun Qiao
Abstract Seeking solitary wave solutions and revealing their interactional characteristics for nonlinear evolution equations help us lot to comprehend the motion laws of the microparticles. As a local nonlinear dynamic behavior, the soliton-collision is difficult to be reproduced numerically. In this paper, the soliton-collision process in the nonlinear perturbed Schrödinger equation is simulated employing the multi-symplectic method. The multi-symplectic formulations are derived including the multi-symplectic form and three local conservation laws of the nonlinear perturbed Schrödinger equation. Employing the implicit midpoint rule, we construct a multi-symplectic scheme, which is equivalent to the Preissmann box scheme, for the nonlinear perturbed Schrödinger equation. The elegant structure-preserving properties of the multi-symplectic scheme are illustrated by the tiny maximum absolute residual of the discrete multi-symplectic structure at each time step in the numerical simulations. The effects of the perturbation strength on the soliton-collision in the nonlinear perturbed Schrödinger equation are reported in the numerical results in detail.
{"title":"Multi-Symplectic Simulation on Soliton-Collision for Nonlinear Perturbed Schrödinger Equation","authors":"Peijun Zhang, Weipeng Hu, Zhen Wang, Zhijun Qiao","doi":"10.1007/s44198-023-00137-1","DOIUrl":"https://doi.org/10.1007/s44198-023-00137-1","url":null,"abstract":"Abstract Seeking solitary wave solutions and revealing their interactional characteristics for nonlinear evolution equations help us lot to comprehend the motion laws of the microparticles. As a local nonlinear dynamic behavior, the soliton-collision is difficult to be reproduced numerically. In this paper, the soliton-collision process in the nonlinear perturbed Schrödinger equation is simulated employing the multi-symplectic method. The multi-symplectic formulations are derived including the multi-symplectic form and three local conservation laws of the nonlinear perturbed Schrödinger equation. Employing the implicit midpoint rule, we construct a multi-symplectic scheme, which is equivalent to the Preissmann box scheme, for the nonlinear perturbed Schrödinger equation. The elegant structure-preserving properties of the multi-symplectic scheme are illustrated by the tiny maximum absolute residual of the discrete multi-symplectic structure at each time step in the numerical simulations. The effects of the perturbation strength on the soliton-collision in the nonlinear perturbed Schrödinger equation are reported in the numerical results in detail.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135254857","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}
Pub Date : 2023-08-05DOI: 10.1007/s44198-023-00133-5
Tao-Qian Tang, Rashid Jan, H. Ahmad, Z. Shah, N. Vrinceanu, Mihaela Racheriu
{"title":"A Fractional Perspective on the Dynamics of HIV, Considering the Interaction of Viruses and Immune System with the Effect of Antiretroviral Therapy","authors":"Tao-Qian Tang, Rashid Jan, H. Ahmad, Z. Shah, N. Vrinceanu, Mihaela Racheriu","doi":"10.1007/s44198-023-00133-5","DOIUrl":"https://doi.org/10.1007/s44198-023-00133-5","url":null,"abstract":"","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46914146","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}
Pub Date : 2023-07-31DOI: 10.1007/s44198-023-00131-7
B. Juárez-Campos, J. Villela‐Aguilar, Rafael Carreño-Bolaños
{"title":"Asymptotics of Solutions for Periodic Problem for the Korteweg-de Vries Equation with Landau Damping, Pumping and Higher Order Convective Non Linearity","authors":"B. Juárez-Campos, J. Villela‐Aguilar, Rafael Carreño-Bolaños","doi":"10.1007/s44198-023-00131-7","DOIUrl":"https://doi.org/10.1007/s44198-023-00131-7","url":null,"abstract":"","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52860191","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}
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