When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The q...When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The quintic B-spline collocation method is used for solving such nonlinear partial differential equations. The developed plan uses the collocation approach and finite difference method to solve the problem under consideration. The given problem is discretized in both time and space directions. Forward difference formula is used for temporal discretization. Collocation method is used for spatial discretization. Additionally, by using Von Neumann stability analysis, it is demonstrated that the devised scheme is stable and convergent with regard to time. Examining two analytical approaches to show the effectiveness and performance of our approximate solution.展开更多
Travelling wave solutions have been played a vital role in demonstrating the wave character of nonlinear problems arising in the field of ocean engineering and sciences.To describe the propagation of the nonlinear wav...Travelling wave solutions have been played a vital role in demonstrating the wave character of nonlinear problems arising in the field of ocean engineering and sciences.To describe the propagation of the nonlinear wave phenomenon in the ocean(for example,wind waves,tsunami waves),a variety of evolution equations have been suggested and investigated in the existing literature.This paper studies the dynamic of travelling periodic and solitary wave behavior of a double-dispersive non-linear evolution equation,named the Sharma-Tasso-Olver(STO)equation.Nonlinear evolution equations with double dispersion enable us to describe nonlinear wave propagation in the ocean,hyperplastic rods and other mediums in the field of science and engineering.We analyze the wave solutions of this model using a combination of numerical simulations and Ansatz techniques.Our analysis shows that the travelling wave solutions involve a range of parameters that displays important and very interesting properties of the wave phenomena.The relevance of the parameters in the travelling wave solutions is also discussed.By simulating numerically,we demonstrate how parameters in the solutions influence the phase speed as well as the travelling and solitary waves.Furthermore,we discuss instantaneous streamline patterns among the obtained solutions to explore the local direction of the components of the obtained solitary wave solutions at each point in the coordinate(x,t).展开更多
By applying the fermionization approach, the inverse version of the bosoniza- tion approach, to the Sharma-Tasso-Olver （STO） equation, three simple supersymmetric extensions of the STO equation are obtained from the...By applying the fermionization approach, the inverse version of the bosoniza- tion approach, to the Sharma-Tasso-Olver （STO） equation, three simple supersymmetric extensions of the STO equation are obtained from the Painlee analysis. Furthermore, some types of special exact solutions to the supersymmetric extensions are obtained.展开更多
文摘When analysing the thermal conductivity of magnetic fluids, the traditional Sharma-Tasso-Olver (STO) equation is crucial. The Sharma-Tasso-Olive equation’s approximate solution is the primary goal of this work. The quintic B-spline collocation method is used for solving such nonlinear partial differential equations. The developed plan uses the collocation approach and finite difference method to solve the problem under consideration. The given problem is discretized in both time and space directions. Forward difference formula is used for temporal discretization. Collocation method is used for spatial discretization. Additionally, by using Von Neumann stability analysis, it is demonstrated that the devised scheme is stable and convergent with regard to time. Examining two analytical approaches to show the effectiveness and performance of our approximate solution.
文摘Travelling wave solutions have been played a vital role in demonstrating the wave character of nonlinear problems arising in the field of ocean engineering and sciences.To describe the propagation of the nonlinear wave phenomenon in the ocean(for example,wind waves,tsunami waves),a variety of evolution equations have been suggested and investigated in the existing literature.This paper studies the dynamic of travelling periodic and solitary wave behavior of a double-dispersive non-linear evolution equation,named the Sharma-Tasso-Olver(STO)equation.Nonlinear evolution equations with double dispersion enable us to describe nonlinear wave propagation in the ocean,hyperplastic rods and other mediums in the field of science and engineering.We analyze the wave solutions of this model using a combination of numerical simulations and Ansatz techniques.Our analysis shows that the travelling wave solutions involve a range of parameters that displays important and very interesting properties of the wave phenomena.The relevance of the parameters in the travelling wave solutions is also discussed.By simulating numerically,we demonstrate how parameters in the solutions influence the phase speed as well as the travelling and solitary waves.Furthermore,we discuss instantaneous streamline patterns among the obtained solutions to explore the local direction of the components of the obtained solitary wave solutions at each point in the coordinate(x,t).
基金Project supported by the National Natural Science Foundation of China (Nos.10735030,11175092)the National Basic Research Program of China (Nos.2007CB814800,2005CB422301)K.C.Wong Magna Fund in Ningbo University
文摘By applying the fermionization approach, the inverse version of the bosoniza- tion approach, to the Sharma-Tasso-Olver （STO） equation, three simple supersymmetric extensions of the STO equation are obtained from the Painlee analysis. Furthermore, some types of special exact solutions to the supersymmetric extensions are obtained.
