The nonlinear dispersive modified Benjamin-Bona-Mahony(DMBBM)equation is solved numerically using adaptive moving mesh PDEs(MMPDEs)method.Indeed,the exact solution of the DMBBM equation is obtained by using the extend...The nonlinear dispersive modified Benjamin-Bona-Mahony(DMBBM)equation is solved numerically using adaptive moving mesh PDEs(MMPDEs)method.Indeed,the exact solution of the DMBBM equation is obtained by using the extended Jacobian elliptic function expansion method.The current methods give a wider applicability for handling nonlinear wave equations in engineering and mathematical physics.The adaptive moving mesh method is compared with exact solution by numerical examples,where the explicit solutions are known.The numerical results verify the accuracy of the proposed method.展开更多
The extraction of traveling wave solutions for nonlinear evolution equations is a challenge in various mathematics,physics,and engineering disciplines.This article intends to analyze several traveling wave solutions f...The extraction of traveling wave solutions for nonlinear evolution equations is a challenge in various mathematics,physics,and engineering disciplines.This article intends to analyze several traveling wave solutions for themodified regularized long-wave(MRLW)equation using several approaches,namely,the generalized algebraic method,the Jacobian elliptic functions technique,and the improved Q-expansion strategy.We successfully obtain analytical solutions consisting of rational,trigonometric,and hyperbolic structures.The adaptive moving mesh technique is applied to approximate the numerical solution of the proposed equation.The adaptive moving mesh method evenly distributes the points on the high error areas.This method perfectly and strongly reduces the error.We compare the constructed exact and numerical results to ensure the reliability and validity of the methods used.To better understand the considered equation’s physical meaning,we present some 2D and 3D figures.The exact and numerical approaches are efficient,powerful,and versatile for establishing novel bright,dark,bell-kink-type,and periodic traveling wave solutions for nonlinear PDEs.展开更多
Phytoplanktons are drifting plants in an aquatic system.They provide food for marine animals and are compared to terrestrial plants in that having chlorophyll and carrying out photosynthesis.Zooplanktons are drifting ...Phytoplanktons are drifting plants in an aquatic system.They provide food for marine animals and are compared to terrestrial plants in that having chlorophyll and carrying out photosynthesis.Zooplanktons are drifting animals found inside the aquatic bodies.For stable aquatic ecosystem,the growth of both Zooplankton and Phytoplankton should be in steady state but in previous eras,there has been a universal explosion in destructive Plankton or algal blooms.Many investigators used various mathematical methodologies to try to explain the bloom phenomenon.So,in this paper,a discretized two-dimensional Phytoplankton-Zooplankton model is investigated.The results for the existence and uniqueness,and conditions for local stability with topological classifications of the equilibrium solutions are determined.It is also exhibited that at trivial and semitrivial equilibrium solutions,discrete model does not undergo fip bifurcation,but it undergoes Neimark-Sacker bifurcation at interior equilibrium solution under certain conditions.Further,state feedback method is deployed to control the chaos in the under consideration system.The extensive numerical simulations are provided to demonstrate theoretical results.展开更多
文摘The nonlinear dispersive modified Benjamin-Bona-Mahony(DMBBM)equation is solved numerically using adaptive moving mesh PDEs(MMPDEs)method.Indeed,the exact solution of the DMBBM equation is obtained by using the extended Jacobian elliptic function expansion method.The current methods give a wider applicability for handling nonlinear wave equations in engineering and mathematical physics.The adaptive moving mesh method is compared with exact solution by numerical examples,where the explicit solutions are known.The numerical results verify the accuracy of the proposed method.
文摘The extraction of traveling wave solutions for nonlinear evolution equations is a challenge in various mathematics,physics,and engineering disciplines.This article intends to analyze several traveling wave solutions for themodified regularized long-wave(MRLW)equation using several approaches,namely,the generalized algebraic method,the Jacobian elliptic functions technique,and the improved Q-expansion strategy.We successfully obtain analytical solutions consisting of rational,trigonometric,and hyperbolic structures.The adaptive moving mesh technique is applied to approximate the numerical solution of the proposed equation.The adaptive moving mesh method evenly distributes the points on the high error areas.This method perfectly and strongly reduces the error.We compare the constructed exact and numerical results to ensure the reliability and validity of the methods used.To better understand the considered equation’s physical meaning,we present some 2D and 3D figures.The exact and numerical approaches are efficient,powerful,and versatile for establishing novel bright,dark,bell-kink-type,and periodic traveling wave solutions for nonlinear PDEs.
基金The research of A.Q.Khan and F.Nazir is partially supported by the Higher Education Commission of Pakistan.
文摘Phytoplanktons are drifting plants in an aquatic system.They provide food for marine animals and are compared to terrestrial plants in that having chlorophyll and carrying out photosynthesis.Zooplanktons are drifting animals found inside the aquatic bodies.For stable aquatic ecosystem,the growth of both Zooplankton and Phytoplankton should be in steady state but in previous eras,there has been a universal explosion in destructive Plankton or algal blooms.Many investigators used various mathematical methodologies to try to explain the bloom phenomenon.So,in this paper,a discretized two-dimensional Phytoplankton-Zooplankton model is investigated.The results for the existence and uniqueness,and conditions for local stability with topological classifications of the equilibrium solutions are determined.It is also exhibited that at trivial and semitrivial equilibrium solutions,discrete model does not undergo fip bifurcation,but it undergoes Neimark-Sacker bifurcation at interior equilibrium solution under certain conditions.Further,state feedback method is deployed to control the chaos in the under consideration system.The extensive numerical simulations are provided to demonstrate theoretical results.
