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Abundant closed-form wave solutions and dynamical structures of soliton solutions to the (3+1)-dimensional BLMP equation in mathematical physics

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Journal of Ocean Engineering and Science 2022年第2期7卷 178-187页

作者： Sachin Kumar Amit Kumar Department of Mathematics Faculty of Mathematical SciencesUniversity of DelhiDelhi 110007India Department of Mathematics Sri Vankateswara CollegeUniversity of DelhiDelhi 110021India

The physical principles of natural occurrences are frequently examined using nonlinear evolution equa-tions(NLEEs).Nonlinear equations are intensively investigated in mathematical physics,ocean physics,scientific applications,and marine engineering.This paper investigates the Boiti-Leon-Manna-Pempinelli(BLMP)equation in(3+1)-dimensions,which describes fluid propagation and can be considered as a non-linear complex physical model for incompressible fluids in plasma physics.This four-dimensional BLMP equation is certainly a dynamical nonlinear evolution equation in real-world applications.Here,we im-plement the generalized exponential rational function(GERF)method and the generalized Kudryashov method to obtain the exact closed-form solutions of the considered BLMP equation and construct novel solitary wave solutions,including hyperbolic and trigonometric functions,and exponential rational func-tions with arbitrary constant parameters.These two efficient methods are applied to extracting solitary wave solutions,dark-bright solitons,singular solitons,combo singular solitons,periodic wave solutions,singular bell-shaped solitons,kink-shaped solitons,and rational form solutions.Some three-dimensional graphics of obtained exact analytic solutions are presented by considering the suitable choice of involved free parameters.Eventually,the established results verify the capability,efficiency,and trustworthiness of the implemented methods.The techniques are effective,authentic,and straightforward mathematical tools for obtaining closed-form solutions to nonlinear partial differential equations(NLPDEs)arising in nonlinear sciences,plasma physics,and fluid dynamics.

关键词： closed-form solutions Generalized exponential rational function method Solitons Generalized Kudryashov method Solitary waves

Specific wave profiles and closed-form soliton solutions for generalized nonlinear wave equation in(3+1)-dimensions with gas bubbles in hydrodynamics and fluids

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Journal of Ocean Engineering and Science 2023年第1期8卷 91-102页

作者： Sachin Kumar Ihsanullah Hamid M.A.Abdou Department of Mathematics Faculty of Mathematical SciencesUniversity of DelhiDelhi 110007India Department of Mathematics College of SciencesUniversity of BishaP.O.Box 344Bisha 61922Saudi Arabia Physics Department Faculty of ScienceMansoura UniversityMansoura 35516Egypt

Nonlinear evolution equations(NLEEs)are frequently employed to determine the fundamental principles of natural phenomena.Nonlinear equations are studied extensively in nonlinear sciences,ocean physics,fluid dynamics,plasma physics,scientific applications,and marine engineering.The generalized exponen-tial rational function(GERF)technique is used in this article to seek several closed-form wave solutions and the evolving dynamics of different wave profiles to the generalized nonlinear wave equation in(3+1)dimensions,which explains several more nonlinear phenomena in liquids,including gas bubbles.A large number of closed-form wave solutions are generated,including trigonometric function solutions,hyper-bolic trigonometric function solutions,and exponential rational functional solutions.In the dynamics of distinct solitary waves,a variety of soliton solutions are obtained,including single soliton,multi-wave structure soliton,kink-type soliton,combo singular soliton,and singularity-form wave profiles.These de-termined solutions have never previously been published.The dynamical wave structures of some analyt-ical solutions are graphically demonstrated using three-dimensional graphics by providing suitable values to free parameters.This technique can also be used to obtain the soliton solutions of other well-known equations in engineering physics,fluid dynamics,and other fields of nonlinear sciences.

关键词： closed-form solutions Dynamical wave patterns Analytic solutions Nonlinear wave equation GERF Method Solitary waves Solitons

closed-form solutions FOR ELASTOPLASTIC PURE BENDING OF A CURVED BEAM WITH MATERIAL INHOMOGENEITY

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Acta Mechanica Solida Sinica 2014年第1期27卷 54-64页

作者： Guojuan Nie Zheng Zhong School of Aerospace Engineering and Applied Mechanics Tongji University

The elastoplastic pure bending problem of a curved beam with material inhomo- geneity is investigated based on Tresca＇s yield criterion and its associated flow rule. Suppose that the material is elastically isotropic, ideally elastic-plastic and its elastic modulus and yield limit vary radially according to exponential functions. closed-form solutions to the stresses and radial displacement in both purely elastic stress state and partially plastic stress state are presented. Numerical examples reveal the distinct characteristics of elastoplastic bending of a curved beam composed of inhomogeneous materials. Due to the inhomogeneity of materials, the bearing capac- ity of the curved beam can be improved greatly and the initial yield mode can also be dominated. closed-form solutions presented here can serve as benchmark results for evaluating numerical solutions.

关键词： elastoplastic pure bending curved beam inhomogeneous materials closed-form solutions

Evolutionary dynamics of solitary wave profiles and abundant analytical solutions to a(3+1)-dimensional burgers system in ocean physics and hydrodynamics

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Journal of Ocean Engineering and Science 2023年第1期8卷 1-14页

作者： Sachin Kumar Amit Kumar Brij Mohan Department of Mathematics Faculty of Mathematical SciencesUniversity of DelhiDelhi 110007India Department of Mathematics Sri Vankateswara CollegeUniversity of DelhiDelhi 110021India Department of Mathematics Hansraj CollegeUniversity of DelhiDelhi 110007India

In the fields of oceanography,hydrodynamics,and marine engineering,many mathematicians and physi-cists are interested in Burgers-type equations to show the different dynamics of nonlinear wave phenom-ena,one of which is a(3+1)-dimensional Burgers system that is currently being studied.In this paper,we apply two different analytical methods,namely the generalized Kudryashov(GK)method,and the generalized exponential rational function method,to derive abundant novel analytic exact solitary wave solutions,including multi-wave solitons,multi-wave peakon solitons,kink-wave profiles,stripe solitons,wave-wave interaction profiles,and periodic oscillating wave profiles for a(3+1)-dimensional Burgers sys-tem with the assistance of symbolic computation.By employing the generalized Kudryashov method,we obtain some new families of exact solitary wave solutions for the Burgers system.Further,we applied the generalized exponential rational function method to obtain a large number of soliton solutions in the forms of trigonometric and hyperbolic function solutions,exponential rational function solutions,peri-odic breather-wave soliton solutions,dark and bright solitons,singular periodic oscillating wave soliton solutions,and complex multi-wave solutions under various family cases.Based on soft computing via Wolfram Mathematica,all the newly established solutions are verified by back substituting them into the considered Burgers system.Eventually,the dynamical behaviors of some established results are exhibited graphically through three-and two-dimensional wave profiles via numerical simulation.

关键词： Dynamical structures Burger system GERF Method Generalized kudryashov method closed-form solutions Solitary waves

Bio-inspired Topological Skeleton for the Analysis of Quadruped Kinematic Gait

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Journal of Bionic Engineering 2018年第5期15卷 839-850页

作者： Benjamin Boudon Jean-Marc Linares Anick Abourachid Arthur Vauquelin Emmanuel Mermoz Aix Marseille University CNRS ISM Marseille 13009 France Museum National d'Histoire Naturelle Pavillon d'Anatomie Comparbe 57 rue Cuvier F-75231 Paris Cedex 05 France Airbus Helicopters Abroport de Marseille Provence Marignane 13700 France

In bio-inspired design activities, nature is a basis of knowledge. Over the last twenty years, many solutions to measure and analyze human or animal gaits have been developed （VICON system, X-ray radiography...）. Although, these methods are becoming more and more accurate, they are quite expensive, long to set up and not easily portable. In this paper, a method called the bio-inspired topological skeleton is proposed in order to complement the classic videography process and to enable animal gait analysis. A new predictive kinematic model with closed-loops of an unguligrade quadruped is suggested. This kinematic model includes three segments per leg and takes into account the scapula movements. The proposed method allows us to improve the accuracy of the kinematic input data measured from a single video including an additional artefact. To show the benefits of this method, joint parameters that are difficult to measure are derived symbolically from the kinematic model and compared with experimental data.

关键词： quadruped locomotion motion analysis topological skeleton closed-form solutions Multibody Systems （MBS）

A Continuous Solution Design for Two-Dimensional Navier-Stokes Equations

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A Continuous Solution Design for Two-Dimensional Navier-Stok...

SEISMIC ANALYSES FOR OVALING DEformATION OF CIRCULAR TUNNELS IN NO-SLIP CONDITION

第五届海峡两岸水动力学研讨会

作者： Yung Yu Chen Department of Systems and Naval Mechatronic Engineering National Cheng Kung University

A new methodology via using a combination of the fuzzy interpolation algorithm and optimization method to obtain the closed-form solutions of"Two-dimensional Navier-Stokes equations"（2-D NSE）is presented in this investigation.The design objective is to find two fuzzy solutions to satisfy precisely the 2-D NSE frequently encountered in practical applications.In this study,a rough fuzzy solution is formulated with designable parameters firstly,and then,closed-form solutions for the free parameters in the consequent parts of the proposed fuzzy solutions are derived from minimizing an error cost function and the constrained boundary conditions which is the square summation of approximation errors of boundary conditions,continuum equation and Navier-Stokes equations.In addition,elegant approximated error bounds between the exact solution and the proposed fuzzy solution with respect to the number of fuzzy rules and solution errors have also been proven.Furthermore,the error equations in mesh points can be proven to converge to zero for the2-D NSE without making assumptions.

关键词： Navier-Stokes equations Optimal method Fuzzy interpolation closed-form solutions

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SEISMIC ANALYSES FOR OVALING DEFORMATION OF CIRCULAR TUNNELS...