Pub Date : 2023-10-30DOI: 10.1007/s44198-023-00149-x
Ling Lei, Shou-Fu Tian, Yan-Qiang Wu
Abstract We investigate the multi-soliton solutions for the Cauchy problem of the nonlocal Kundu-nonlinear Schrödinger (NK-NLS) equation with step-like initial data. We first perform the spectral analysis on the Lax pair of the NK-NLS equation, and then establish the Riemann-Hilbert (RH) problem of the equation based on the analytic, symmetric and asymptotic properties of Jost solutions and spectral functions. Because of the influence of step-like initial value, we need to consider the singularity condition of the RH problem at the origin, and this singularity condition can be converted to a residue condition. Further, the multi-soliton solutions of the NK-NLS equation are obtained in terms of the corresponding RH problem.
{"title":"Multi-Soliton Solutions for the Nonlocal Kundu-Nonlinear Schrödinger Equation with Step-Like Initial Data","authors":"Ling Lei, Shou-Fu Tian, Yan-Qiang Wu","doi":"10.1007/s44198-023-00149-x","DOIUrl":"https://doi.org/10.1007/s44198-023-00149-x","url":null,"abstract":"Abstract We investigate the multi-soliton solutions for the Cauchy problem of the nonlocal Kundu-nonlinear Schrödinger (NK-NLS) equation with step-like initial data. We first perform the spectral analysis on the Lax pair of the NK-NLS equation, and then establish the Riemann-Hilbert (RH) problem of the equation based on the analytic, symmetric and asymptotic properties of Jost solutions and spectral functions. Because of the influence of step-like initial value, we need to consider the singularity condition of the RH problem at the origin, and this singularity condition can be converted to a residue condition. Further, the multi-soliton solutions of the NK-NLS equation are obtained in terms of the corresponding RH problem.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136022603","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 : 2023-10-19DOI: 10.1007/s44198-023-00138-0
H. Amirzadeh-Fard, Gh. Haghighatdoost, A. Rezaei-Aghdam
Abstract By Poissonization of Jacobi structures on real three-dimensional Lie groups $${textbf{G}}$$ G and using the realizations of their Lie algebras, we obtain integrable bi-Hamiltonian systems on $${textbf{G}} otimes {mathbb {R}}$$ G⊗R .
{"title":"Integrable Bi-Hamiltonian Systems by Jacobi Structure on Real Three-Dimensional Lie Groups","authors":"H. Amirzadeh-Fard, Gh. Haghighatdoost, A. Rezaei-Aghdam","doi":"10.1007/s44198-023-00138-0","DOIUrl":"https://doi.org/10.1007/s44198-023-00138-0","url":null,"abstract":"Abstract By Poissonization of Jacobi structures on real three-dimensional Lie groups $${textbf{G}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>G</mml:mi> </mml:math> and using the realizations of their Lie algebras, we obtain integrable bi-Hamiltonian systems on $${textbf{G}} otimes {mathbb {R}}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo>⊗</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> .","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135730560","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 : 2023-10-19DOI: 10.1007/s44198-023-00146-0
M. M. Khader, M. M. Babatin
Abstract This study aims to elucidates the effects of Ohmic dissipation and the magnetic field on the behavior of a Casson fluid flowing across a vertically stretched surface. The goal is to solve the problem by using numerical approaches. Furthermore, the fluid’s thermal conductivity is intended to vary proportionately with temperature. The effects of thermal radiation, electric fields, and viscous dissipation are taken into account in this study. A set of partial differential equations (PDEs) is used to quantitatively reflect the numerous physical conditions that are placed on the sheet’s surrounding wall as well as the processes of momentum and heat transport. A system of ordinary differential equations (ODEs) is created from the set of PDEs by using similarity transformations. The mathematical model of the problem is made easier by this conversion. Furthermore, this study’s main goal is to investigate the numerical treatment of the proposed model that takes Caputo fractional-order derivatives into account. The spectral collocation method is used to solve the system of ODEs that follow from the transformation. This approach efficiently solves the problem by approximating the solution of the ODEs using Chebyshev polynomials of the sixth kind. Several observations are made to evaluate the approach’s effectiveness, and the convergence of the method is studied. Visual representations of the effects of different parameters on the velocity and temperature profiles provide a thorough understanding of their effects. These graphical representations offer insightful views into how the system behaves in various scenarios. The results of this investigation suggest that the mixed convection parameter and the local electric parameter both boost the velocity field. Further, the temperature field is positively impacted by the slip velocity, thermal conductivity, and Eckert numbers. These findings imply that altering these variables will have an impact on the system’s fluid flow and heat transfer properties.
{"title":"Evaluating the Impacts of Thermal Conductivity on Casson Fluid Flow Near a Slippery Sheet: Numerical Simulation Using Sixth-Kind Chebyshev Polynomials","authors":"M. M. Khader, M. M. Babatin","doi":"10.1007/s44198-023-00146-0","DOIUrl":"https://doi.org/10.1007/s44198-023-00146-0","url":null,"abstract":"Abstract This study aims to elucidates the effects of Ohmic dissipation and the magnetic field on the behavior of a Casson fluid flowing across a vertically stretched surface. The goal is to solve the problem by using numerical approaches. Furthermore, the fluid’s thermal conductivity is intended to vary proportionately with temperature. The effects of thermal radiation, electric fields, and viscous dissipation are taken into account in this study. A set of partial differential equations (PDEs) is used to quantitatively reflect the numerous physical conditions that are placed on the sheet’s surrounding wall as well as the processes of momentum and heat transport. A system of ordinary differential equations (ODEs) is created from the set of PDEs by using similarity transformations. The mathematical model of the problem is made easier by this conversion. Furthermore, this study’s main goal is to investigate the numerical treatment of the proposed model that takes Caputo fractional-order derivatives into account. The spectral collocation method is used to solve the system of ODEs that follow from the transformation. This approach efficiently solves the problem by approximating the solution of the ODEs using Chebyshev polynomials of the sixth kind. Several observations are made to evaluate the approach’s effectiveness, and the convergence of the method is studied. Visual representations of the effects of different parameters on the velocity and temperature profiles provide a thorough understanding of their effects. These graphical representations offer insightful views into how the system behaves in various scenarios. The results of this investigation suggest that the mixed convection parameter and the local electric parameter both boost the velocity field. Further, the temperature field is positively impacted by the slip velocity, thermal conductivity, and Eckert numbers. These findings imply that altering these variables will have an impact on the system’s fluid flow and heat transfer properties.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135729670","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 : 2023-10-18DOI: 10.1007/s44198-023-00144-2
Ming Li, Jianxia He
Abstract This paper is devoted to the stability and decay estimates of solutions to the two-dimensional magneto-micropolar fluid equations with partial dissipation. Firstly, focus on the 2D magneto-micropolar equation with only velocity dissipation and partial magnetic diffusion, we obtain the global existence of solutions with small initial in $$H^s({mathbb {R}}^2)$$ Hs(R2) $$(s>1)$$ (s>1) , and by fully exploiting the special structure of the system and using the Fourier splitting methods, we establish the large time decay rates of solutions. Secondly, when the magnetic field has partial dissipation, we show the global existence of solutions with small initial data in $$dot{B}^0_{2,1}({mathbb {R}}^2)$$ B˙2,10(R2) . In addition, we explore the decay rates of these global solutions are correspondingly established in $$dot{B}^m_{2,1}({mathbb {R}}^2)$$ B˙2,1m(R2) with $$0 le m le s$$ 0≤m≤s , when the initial data belongs to the negative Sobolev space $$dot{H}^{-l}({mathbb {R}}^2)$$ H˙-l(R2) (for each $$0 le l <1$$ 0≤
摘要本文研究具有部分耗散的二维磁微极流体方程解的稳定性和衰减估计。首先，对只考虑速度耗散和部分磁扩散的二维磁微极方程，得到了在$$H^s({mathbb {R}}^2)$$ H s (R 2) $$(s>1)$$ (s ＆gt;1)，充分利用系统的特殊结构，利用傅里叶分裂方法，建立了解的大时间衰减率。其次，当磁场存在部分耗散时，我们在$$dot{B}^0_{2,1}({mathbb {R}}^2)$$ B˙2,10 (r2)中证明了具有小初始数据的解的整体存在性。此外，我们还探讨了当初始数据属于负Sobolev空间$$dot{H}^{-l}({mathbb {R}}^2)$$ H˙l (r2)时，这些全局解的衰减率对应地建立在$$dot{B}^m_{2,1}({mathbb {R}}^2)$$ B˙2,1 m (r2)中，$$0 le m le s$$ 0≤m≤s(对于每个$$0 le l <1$$ 0≤l ＆lt;1)。
{"title":"Large Time Behavior and Stability for Two-Dimensional Magneto-Micropolar Equations with Partial Dissipation","authors":"Ming Li, Jianxia He","doi":"10.1007/s44198-023-00144-2","DOIUrl":"https://doi.org/10.1007/s44198-023-00144-2","url":null,"abstract":"Abstract This paper is devoted to the stability and decay estimates of solutions to the two-dimensional magneto-micropolar fluid equations with partial dissipation. Firstly, focus on the 2D magneto-micropolar equation with only velocity dissipation and partial magnetic diffusion, we obtain the global existence of solutions with small initial in $$H^s({mathbb {R}}^2)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mi>s</mml:mi> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> $$(s>1)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>s</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , and by fully exploiting the special structure of the system and using the Fourier splitting methods, we establish the large time decay rates of solutions. Secondly, when the magnetic field has partial dissipation, we show the global existence of solutions with small initial data in $$dot{B}^0_{2,1}({mathbb {R}}^2)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msubsup> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . In addition, we explore the decay rates of these global solutions are correspondingly established in $$dot{B}^m_{2,1}({mathbb {R}}^2)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msubsup> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mi>m</mml:mi> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> with $$0 le m le s$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>m</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:math> , when the initial data belongs to the negative Sobolev space $$dot{H}^{-l}({mathbb {R}}^2)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mover> <mml:mi>H</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mrow> <mml:mo>-</mml:mo> <mml:mi>l</mml:mi> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> (for each $$0 le l <1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≤</mml:m","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135884418","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 : 2023-10-16DOI: 10.1007/s44198-023-00145-1
M. Ferdows, Abid Hossain, M. J. Uddin, Fahiza Tabassum Mim, Shuyu Sun
Abstract The viscous laminar magnetohydrodynamic convective boundary layer flow with the combined effects of chemical reaction and nonlinear velocity slip and linear thermal and concentration slips have been considered across a flat plate in motion. Using a non-dimensional transformation attained by the single parameter continuous group method, the governing equations are transformed into a system of nonlinear ordinary similarity equations, then, the solutions of the coupled system of equations are constructed for velocity, temperature, and concentration functions by using the numerical methods. Among the parameters that have been looked at are the buoyancy parameter N, the nonlinear slip parameter $${mathrm{n}}_{1}$$ n1 , the order of chemical reaction n, the Prandtl number Pr, and the Schmidt number Sc. An investigation was made on the profiles with respect to mixed convection parameter $$uplambda $$ λ , order of chemical reaction n, arbitrary index parameter $${mathrm{n}}_{1}$$ n1 , velocity slip parameter a, thermal slip parameter b, mass slip parameter c, suction parameter fw, magnetic parameter M. Verification of the results were possible due to comparison of two numerical methods to obtain the solution to the differential equations. The present study indicates that, for a range of values of the magnetic parameter, the wall shear stress decreases with increasing mixed convection. Moreover, for a variety of mixed convection parameter instances, the wall heat transfer decreases with increasing perpendicular magnetic effect.
摘要研究了在运动平板上具有化学反应、非线性速度滑移和线性热、浓度滑移共同作用的粘性层流磁流体动力对流边界层流动。利用单参数连续群法得到的无量纲变换，将控制方程转化为非线性普通相似方程组，然后用数值方法构造速度、温度和浓度函数耦合方程组的解。研究的参数包括浮力参数N、非线性滑移参数$${mathrm{n}}_{1}$$ N 1、化学反应阶数N、普朗特数Pr和施密特数Sc。研究了混合对流参数$$uplambda $$ λ、化学反应阶数N、任意指标参数$${mathrm{n}}_{1}$$ N 1、速度滑移参数a、热滑移参数b、质量滑移参数c、通过比较两种数值方法求得的微分方程的解，可以对结果进行验证。研究表明，在一定的磁参量范围内，壁面剪切应力随混合对流的增大而减小。在多种混合对流参数情况下，壁面换热随垂直磁效应的增大而减小。
{"title":"New Similarity Solutions of Magnetohydrodynamic Flow Over Horizontal Plate by Lie Group with Nonlinear Hydrodynamic and Linear Thermal and Mass Slips","authors":"M. Ferdows, Abid Hossain, M. J. Uddin, Fahiza Tabassum Mim, Shuyu Sun","doi":"10.1007/s44198-023-00145-1","DOIUrl":"https://doi.org/10.1007/s44198-023-00145-1","url":null,"abstract":"Abstract The viscous laminar magnetohydrodynamic convective boundary layer flow with the combined effects of chemical reaction and nonlinear velocity slip and linear thermal and concentration slips have been considered across a flat plate in motion. Using a non-dimensional transformation attained by the single parameter continuous group method, the governing equations are transformed into a system of nonlinear ordinary similarity equations, then, the solutions of the coupled system of equations are constructed for velocity, temperature, and concentration functions by using the numerical methods. Among the parameters that have been looked at are the buoyancy parameter N, the nonlinear slip parameter $${mathrm{n}}_{1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>n</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> , the order of chemical reaction n, the Prandtl number Pr, and the Schmidt number Sc. An investigation was made on the profiles with respect to mixed convection parameter $$uplambda $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>λ</mml:mi> </mml:math> , order of chemical reaction n, arbitrary index parameter $${mathrm{n}}_{1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>n</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> , velocity slip parameter a, thermal slip parameter b, mass slip parameter c, suction parameter fw, magnetic parameter M. Verification of the results were possible due to comparison of two numerical methods to obtain the solution to the differential equations. The present study indicates that, for a range of values of the magnetic parameter, the wall shear stress decreases with increasing mixed convection. Moreover, for a variety of mixed convection parameter instances, the wall heat transfer decreases with increasing perpendicular magnetic effect.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136113048","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 : 2023-10-10DOI: 10.1007/s44198-023-00147-z
Sheng-Nan Wang, Guo-Fu Yu, Zuo-Nong Zhu
Abstract In this paper, we investigate solutions of a (2+1)-dimensional sinh-Gordon equation. General solitons and (semi-)rational solutions are derived by the combination of Hirota’s bilinear method and Kadomtsev-Petviashvili hierarchy reduction approach. General solutions are expressed as $$Ntimes N$$ N×N Gram-type determinants. When the determinant size N is even, we generate solitons, line breathers, and (semi-)rational solutions located on constant backgrounds. In particular, through the asymptotic analysis we prove that the collision of solitons are completely elastic. When N is odd, we derive exact solutions on periodic backgrounds. The dynamical behaviors of those derived solutions are analyzed with plots. For rational solutions, we display the interaction of lumps. For semi-rational solutions, we find the interaction solutions between lumps and solitons.
摘要本文研究了一类(2+1)维sinh-Gordon方程的解。结合Hirota的双线性方法和Kadomtsev-Petviashvili层次约简方法，导出了一般孤子和(半)有理解。通解表示为$$Ntimes N$$ N × N gram型行列式。当行列式大小N为偶数时，我们生成位于恒定背景上的孤子、线呼吸子和(半)有理解。特别地，我们通过渐近分析证明了孤子的碰撞是完全弹性的。当N为奇数时，我们得到周期背景下的精确解。用图表分析了这些解的动力学行为。对于有理解，我们展示了块的相互作用。对于半有理解，我们找到了块与孤子之间的相互作用解。
{"title":"General Soliton and (Semi-)Rational Solutions of a (2+1)-Dimensional Sinh-Gordon Equation","authors":"Sheng-Nan Wang, Guo-Fu Yu, Zuo-Nong Zhu","doi":"10.1007/s44198-023-00147-z","DOIUrl":"https://doi.org/10.1007/s44198-023-00147-z","url":null,"abstract":"Abstract In this paper, we investigate solutions of a (2+1)-dimensional sinh-Gordon equation. General solitons and (semi-)rational solutions are derived by the combination of Hirota’s bilinear method and Kadomtsev-Petviashvili hierarchy reduction approach. General solutions are expressed as $$Ntimes N$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>×</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> Gram-type determinants. When the determinant size N is even, we generate solitons, line breathers, and (semi-)rational solutions located on constant backgrounds. In particular, through the asymptotic analysis we prove that the collision of solitons are completely elastic. When N is odd, we derive exact solutions on periodic backgrounds. The dynamical behaviors of those derived solutions are analyzed with plots. For rational solutions, we display the interaction of lumps. For semi-rational solutions, we find the interaction solutions between lumps and solitons.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136354703","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 : 2023-10-05DOI: 10.1007/s44198-023-00142-4
W. Abbas, M. A. Ibrahim, O. Mokhtar, Ahmed M. Megahed, Ahmed A. M. Said
Abstract Nanoparticles have the ability to increase the impact of convective heat transfer in the boundary layer region. An investigation is made to analysis of magnetohdrodynamic nanofluid flow with heat and mass transfer over a vertical cone in porous media under the impact of thermal radiations and chemical reaction. In addition, thermal radiations, Hall current, and viscous and Joule dissipations and chemical reaction effects are considered. Considered three different nanoparticles types namely copper, silver, and titanium dioxide with water as base fluid. The governing equations are transformed by similarity transformations into a set of non-linear ordinary differential equations involving variable coefficients. Two numerically approaches are used to solve the transformed boundary layer system Finite Difference Method (FDM) and Chebyshev-Galerkin Method (CGM). As stated in the present analysis, it is appropriate to address a number of physical mechanisms, including velocity, temperature and concentration, as well as closed-form skin friction/mass transfer/heat transfer coefficients. Different comparisons are done with previously published data in order to validate the current study under specific special circumstances, and it is determined that there is a very high degree of agreement. The main results indicated that as the Prandtl number increases, the temperature profile decreases, but it grows for higher values of the thermophoresis parameter, Brownian motion, and Eckert number. Moreover, higher Brownian motion values lead to a less prominent concentration profile. Consequently, this speeds up the cooling process and enhances the surface’s durability and strength.
{"title":"Numerical Analysis of MHD Nanofluid Flow Characteristics with Heat and Mass Transfer over a Vertical Cone Subjected to Thermal Radiations and Chemical Reaction","authors":"W. Abbas, M. A. Ibrahim, O. Mokhtar, Ahmed M. Megahed, Ahmed A. M. Said","doi":"10.1007/s44198-023-00142-4","DOIUrl":"https://doi.org/10.1007/s44198-023-00142-4","url":null,"abstract":"Abstract Nanoparticles have the ability to increase the impact of convective heat transfer in the boundary layer region. An investigation is made to analysis of magnetohdrodynamic nanofluid flow with heat and mass transfer over a vertical cone in porous media under the impact of thermal radiations and chemical reaction. In addition, thermal radiations, Hall current, and viscous and Joule dissipations and chemical reaction effects are considered. Considered three different nanoparticles types namely copper, silver, and titanium dioxide with water as base fluid. The governing equations are transformed by similarity transformations into a set of non-linear ordinary differential equations involving variable coefficients. Two numerically approaches are used to solve the transformed boundary layer system Finite Difference Method (FDM) and Chebyshev-Galerkin Method (CGM). As stated in the present analysis, it is appropriate to address a number of physical mechanisms, including velocity, temperature and concentration, as well as closed-form skin friction/mass transfer/heat transfer coefficients. Different comparisons are done with previously published data in order to validate the current study under specific special circumstances, and it is determined that there is a very high degree of agreement. The main results indicated that as the Prandtl number increases, the temperature profile decreases, but it grows for higher values of the thermophoresis parameter, Brownian motion, and Eckert number. Moreover, higher Brownian motion values lead to a less prominent concentration profile. Consequently, this speeds up the cooling process and enhances the surface’s durability and strength.","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135480700","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/s44198-023-00143-3
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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