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Soliton solutions,travelling wave solutions and conserved quantities for a three-dimensional soliton equation in plasma physics

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Communications in Theoretical Physics 2021年第12期73卷 25-57页

作者： Chaudry Masood Khalique Oke Davies Adeyemo International institute for Symmetry Analysis and mathematical modelling Department of Mathematical SciencesNorth-West UniversityMafikeng CampusPrivate Bag X 2046Mmabatho 2735South Africa

Many physical systems can be successfully modelled using equations that admit the soliton *** addition,equations with soliton solutions have a significant mathematical *** this paper,we study and analyze a three-dimensional soliton equation,which has applications in plasma physics and other nonlinear sciences such as fluid mechanics,atomic physics,biophysics,nonlinear optics,classical and quantum fields ***,solitons and solitary waves have been observed in numerous situations and often dominate long-time *** perform symmetry reductions of the equation via the use of Lie group theory and then obtain analytic solutions through this technique for the very first *** integration of the resulting ordinary differential equation is done which gives new analytic travelling wave solutions that consist of rational function,elliptic functions,elementary trigonometric and hyperbolic functions solutions of the ***,various solitonic solutions are secured with the use of a polynomial complete discriminant system and elementary integral *** solutions comprise dark soliton,doubly-periodic soliton,trigonometric soliton,explosive/blowup and singular *** further exhibit the dynamics of the solutions with pictorial representations and discuss *** conclusion,we contemplate conserved quantities for the equation under study via the standard multiplier approach in conjunction with the homotopy integral *** state here categorically and emphatically that all results found in this study as far as we know have not been earlier obtained and so are new.

关键词： three-dimensional soliton equation Lie group theory conserved quantities soliton and exact travelling wave solutions physics

EMDEN-FOWLER TYPE SYSTEM:NOETHER SYMMETRIES AND FIRST INTEGRALS

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Acta Mathematica Scientia 2012年第5期32卷 1959-1966页

作者： B.Muatjetjeja C.M.Khalique International institute for Symmetry Analysis and mathematical modelling Department of Mathematical SciencesNorth-West UniversityMafikeng CampusPrivate Bag X 2046Mmabatho 2735Republic of South Africa

We classify a generalized coupled singular Emden-Fowler type system ＋a（t）vn=0,v＋b（t）um=0 with respect to the standard first-order Lagrangian according to the Noether point symmetries which it *** integrals of the various cases which admit Noether point symmetries are then *** system was discussed in the literature from the view-point of existence and uniqueness of positive solutions.

关键词： Lagrangian Noether symmetry first integrals Emden-Fowler type system Gauge function

High Accuracy Finite Volume Method for Solving Nonlinear Aeroacoustics Problems on Unstructured Meshes

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Chinese Journal of Aeronautics 2006年第2期19卷 97-104页

作者： Ilya ABALAKIN Alain DERVIEUX Tatiana KOZUBSKAYA institute for mathematical modelling RAS . MoscowRussia INRIA Sophia-Antipolis France institute for mathematical modelling RAS . MoscowRussia

The paper presents a finite volume numerical method universally applicable for solving both linear and nonlinear aeroacoustics problems on arbitrary unstructured meshes. It is based on the vertexcentered multi-parameter scheme offering up to the 6th accuracy order achieved on the Cartesian meshes. An adaptive dissipation is added for the numerical treatment of possible discontinuities. The scheme properties are studied on a series of test cases, its efficiency is demonstrated at simulating the noise suppression in resonance-type liners.

关键词： nonlinear aeroacoustics Euler based models finite volume method high accuracy approximation unstructured meshes liners

Langrangian formulation and solitary wave solutions of a generalized Zakharov–Kuznetsov equation with dual power-law nonlinearity in physical sciences and engineering

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Journal of Ocean Engineering and Science 2023年第2期8卷 152-168页

This paper presents analytical studies carried out explicitly on a higher-dimensional generalized Zakharov–Kuznetsov equation with dual power-law nonlinearity arising in engineering and nonlinear *** obtain analytic solutions for the underlying equation via Lie group approach as well as direct integration ***,we engage the extended Jacobi elliptic cosine and sine amplitude functions expansion technique to seek more exact travelling wave solutions of the equation for some particular ***,we secure,singular and nonsingular(periodic)soliton solutions,cnoidal,snoidal as well as dnoidal wave ***,we depict the dynamics of the solutions using suitable *** application of obtained results in various fields of sciences and engineering are *** conclusion,we construct conserved currents of the aforementioned equation via Noether’s theorem(with Helmholtz criteria)and standard multiplier technique through the homotopy formula.

关键词： Generalized Zakharov-Kuznetsov equation with dual power-law nonlinearity Lie point symmetries Exact solutions Cnoidal and snoidal wave solutions Conserved currents

Analysis of Sakiadis flow of nanofluids with viscous dissipation and Newtonian heating

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Applied Mathematics and Mechanics(English Edition) 2012年第12期33卷 1545-1554页

作者： O.D.MAKINDE institute for Advance Research in mathematical modelling and Computations Cape Peninsula University of TechnologyP.O.Box 1906Bellville 7535South Africa

The combined effects of viscous dissipation and Newtonian heating on bound- ary layer flow over a moving flat plate are investigated for two types of water-based New- tonian nanofluids containing metallic or nonmetallic nanoparticles such as copper （Cu） and titania （Ti02）. The governing partial differential equations are transformed into ordinary differential equations through a similarity transformation and are solved numer- ically by a Runge-Kutta-Fehlberg method with a shooting technique. The conclusions are that the heat transfer rate at the moving plate surface increases with the increases in the nanoparticle volume fraction and the Newtonian heating, while it decreases with the increase in the Brinkmann number. Moreover, the heat transfer rate at the moving plate surface with Cu-water as the working nanofiuid is higher than that with TiO2-water.

关键词： Sakiadis flow nanofluid viscous dissipation Newtonian heating

Applications of cnoidal and snoidal wave solutions via optimal system of subalgebras for a generalized extended (2+1)-D quantum Zakharov-Kuznetsov equation with power-law nonlinearity in oceanography and ocean engineering

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Journal of Ocean Engineering and Science 2024年第2期9卷 126-153页

作者： Oke Davies Adeyemo International institute for Symmetry Analysis and mathematical modelling Department of Mathematical SciencesNorth-West UniversityMafikeng CampusPrivate Bag X 2046Mmabatho 2735Republic of South Africa

The nonlinear evolution equations have a wide range of applications,more precisely in physics,biology,chemistry and engineering *** domain serves as a point of interest to a large extent in the world’s mathematical ***,this paper purveys an analytical study of a generalized extended(2+1)-dimensional quantum Zakharov-Kuznetsov equation with power-law nonlinearity in oceanography and ocean *** Lie group theory of differential equations is utilized to compute an optimal system of one dimension for the Lie algebra of the *** further reduce the equation using the subalgebras ***,more general solutions of the underlying equation are secured for some special cases of n with the use of extended Jacobi function expansion ***,we secure new bounded and unbounded solutions of interest for the equation in various solitonic structures including bright,dark,periodic(cnoidal and snoidal),compact-type as well as singular *** applications of cnoidal and snoidal waves of the model in oceanography and ocean engineering for the first time,are outlined with suitable *** can be of interest to oceanographers and ocean engineers for future ***,to visualize the dynamics of the results found,we present the graphic display of each of the ***,we construct conservation laws of the understudy equation via the application of Noether’s theorem.

关键词： A generalized extended(2+1)-dimensional quantum Zakharov-Kuznetsov equation Lie point symmetries Optimal system of subalgebras Cnoidal and snoidal waves Extended Jacobi function expansion technique Conservation laws

Dynamical Soliton Wave Structures of One-Dimensional Lie Subalgebras via Group-Invariant Solutions of a Higher-Dimensional Soliton Equation with Various Applications in Ocean Physics and Mechatronics Engineering

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Communications on Applied Mathematics and Computation 2022年第4期4卷 1531-1582页

作者： Oke Davies Adeyemo Chaudry Masood Khalique International institute for Symmetry Analysis and mathematical modelling Department of Mathematical SciencesNorth-West UniversityMafikeng CampusPrivate Bag X 2046Mmabatho 2735Republic of South Africa

Having realized various significant roles that higher-dimensional nonlinear partial differ-ential equations(NLPDEs)play in engineering,we analytically investigate in this paper,a higher-dimensional soliton equation,with applications particularly in ocean physics and mechatronics(electrical electronics and mechanical)*** generators of Lie point symmetries of the equation are computed using Lie group analysis of differen-tial *** addition,we construct commutation as well as Lie adjoint representation tables for the nine-dimensional Lie algebra ***,a one-dimensional optimal system of Lie subalgebras is also presented for the soliton *** consequently enables us to generate abundant group-invariant solutions through the reduction of the understudy equation into various ordinary differential equations(ODEs).On solving the achieved nonlinear differential equations,we secure various solitonic *** conse-quence,these solutions containing diverse mathematical functions furnish copious shapes of dynamical wave structures,ranging from periodic,kink and kink-shaped nanopteron,soliton(bright and dark)to breather waves with extensive wave collisions *** physically interpreted the resulting soliton solutions by imploring graphical depictions in three dimensions,two dimensions and density ***,the gained group-invariant solutions involved several arbitrary functions,thus exhibiting rich physical *** also implore the power series technique to solve part of the complicated differential equa-tions and give valid comments on their ***,we outline some applications of our results in ocean physics and mechatronics engineering.

关键词： Higher-dimensional soliton equation Lie group analysis One-dimensional optimal system of Lie subalgebras Exact soliton solutions Conserved currents

Immersed Interface CIP for One Dimensional Hyperbolic Equations

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Communications in Computational Physics 2014年第6期16卷 96-114页

作者： Kazufumi Ito Tomoya Takeuchi Department of Mathematics North Carolina State UniversityRaleighNC 27695USA. Collaborative Research Center for Innovative mathematical modelling Institute of Industrial ScienceUniversity of TokyoTokyoJapan. FIRST Aihara Innovative Mathematical Modelling ProjectJSTKawaguchiJapan.

The immersed interface technique is incorporated into CIP method to solve one-dimensional hyperbolic equations with piecewise constant *** proposed method achieves the third order of accuracy in time and space in the vicinity of the interface where the coefficients have jump discontinuities,which is the same order of accuracy of the standard CIP *** numerical tests are given to verify the accuracy of the proposed method.

关键词： CIP method immersed interface method hyperbolic equations in discontinuous media.

Numerical Analysis and Experimental Verification of the Behaviour of Solid Inclusions in Induction Crucible Furnaces

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Journal of Iron and Steel Research International 2012年第S2期19卷 713-716页

作者： Mcepanskis A Jakovis E Baake B Nacke Laboratory for mathematical modelling of Environmental and Technological Processes University of Latvia institute of Electrotechnology Leibniz University of Hanover

The paper refers to the dynamics of solid inclusion in the turbulent flow of liquid metal in induction furnaces. The numerical analysis is carried out adopting LES-based Euler-Lagrange approach in the limit of dilute *** admixing of carbon particles in induction crucible furnace from the open surface of a melt is *** behaviour of the particles in the bulk of the flow is illustrated as well as compared with the industrial observation of the open surface of the *** paper also contains the description of the novel experimental technique,which is proposed for the verification of the numerical *** experiment deals with ferromagnetic particles in the flow of Wood's metal in the small induction crucible *** experiment confirms the satisfactory agreement with the numerical results.

关键词： induction furnaces turbulent flow solid inclusions carbon LES experimental verification