In this paper, we study the propagation and its failure to propagate (pinning) of a travelling wave in a Nagumo type equation, an equation that describes impulse propagation in nerve axons that also models population ...In this paper, we study the propagation and its failure to propagate (pinning) of a travelling wave in a Nagumo type equation, an equation that describes impulse propagation in nerve axons that also models population growth with Allee effect. An analytical solution is derived for the traveling wave and the work is extended to a discrete formulation with a piecewise linear reaction function. We propose an operator splitting numerical scheme to solve the equation and demonstrate that the wave either propagates or gets pinned based on how the spatial mesh is chosen.展开更多
Travelling Salesman Problem(TSP)is a discrete hybrid optimization problem considered NP-hard.TSP aims to discover the shortest Hamilton route that visits each city precisely once and then returns to the starting point...Travelling Salesman Problem(TSP)is a discrete hybrid optimization problem considered NP-hard.TSP aims to discover the shortest Hamilton route that visits each city precisely once and then returns to the starting point,making it the shortest route feasible.This paper employed a Farmland Fertility Algorithm(FFA)inspired by agricultural land fertility and a hyper-heuristic technique based on the Modified Choice Function(MCF).The neighborhood search operator can use this strategy to automatically select the best heuristic method formaking the best decision.Lin-Kernighan(LK)local search has been incorporated to increase the efficiency and performance of this suggested approach.71 TSPLIB datasets have been compared with different algorithms to prove the proposed algorithm’s performance and efficiency.Simulation results indicated that the proposed algorithm outperforms comparable methods of average mean computation time,average percentage deviation(PDav),and tour length.展开更多
Using Genetic Algorithms (GAs) is a powerful tool to get solution to large scale design optimization problems. This paper used GA to solve complicated design optimization problems in two different applications. The ai...Using Genetic Algorithms (GAs) is a powerful tool to get solution to large scale design optimization problems. This paper used GA to solve complicated design optimization problems in two different applications. The aims are to implement the genetic algorithm to solve these two different (nested) problems, and to get the best or optimization solutions.展开更多
In this paper, the generalized Dodd-Bullough-Mikhailov equation is studied. The existence of periodic wave and unbounded wave solutions is proved by using the method of bifurcation theory of dynamical systems. Under d...In this paper, the generalized Dodd-Bullough-Mikhailov equation is studied. The existence of periodic wave and unbounded wave solutions is proved by using the method of bifurcation theory of dynamical systems. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.Some exact explicit parametric representations of the above travelling solutions are obtained.展开更多
The scientific achievements of travelling waves in a barotropic atmosphere are introduced, including i) the existence conditions of periodic solutions (wavetrain solutions) and solitary wave solutions (pulse solutions...The scientific achievements of travelling waves in a barotropic atmosphere are introduced, including i) the existence conditions of periodic solutions (wavetrain solutions) and solitary wave solutions (pulse solutions), together with the solution finding methods and a series of related problems, ii) seeking solutions of monotonous wave (wave front) and of nonmonotonous travelling wave (oscillatory wave) by using phase plane shooting technique and hi) progress in the study of travelling wave solution at home and abroad. The investigation of travelling wave solutions in recent years has been found in mathematics, physics, chemistry, biology and other sciences. Over the past decade the problem has been the subject of much interest and become an important area of research. So it is no doubt of great significance to investigate the travelling wave solutions and thereby explain phenomena of weather.展开更多
The travelling wave solutions (TWS) in a class of P. D. E. is studied. The travelling wave equation of this P. D. E. is a planar cubic polynomial system in three-parameter space. The study for M became the topological...The travelling wave solutions (TWS) in a class of P. D. E. is studied. The travelling wave equation of this P. D. E. is a planar cubic polynomial system in three-parameter space. The study for M became the topological classifications of bifurcations of phase portraits defined by the planar system. B using the theory of planar dynamical systems to do qualitative analysis, all topological classifications of the cubic polynomial system can be obtained. Returning the results of the phase plane analysis to TWS, u(xi), and considering discontinuity of the right side of the equation of TWS when xi = x - ct is varied along a phase orbit and passing through a singular curve, all conditions of existence of smooth and nonsmooth travelling waves are given.展开更多
A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a (1+1)-dimensional dispersive long wave equation with general coefficients to an elementary integral fo...A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a (1+1)-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems.展开更多
In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for th...In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.展开更多
Under the travelling wave transformation, the Camassa-Holm equation with dispersion is reduced to an integrable ordinary differential equation (ODE), whose general solution can be obtained using the trick of one-par...Under the travelling wave transformation, the Camassa-Holm equation with dispersion is reduced to an integrable ordinary differential equation (ODE), whose general solution can be obtained using the trick of one-parameter group. Furthermore, by using a complete discrimination system for polynomial, the classification of all single travelling wave solutions to the Camassa-Holm equation with dispersion is obtained. In particular, an affine subspace structure in the set of the solutions of the reduced ODE is obtained. More generally, an implicit linear structure in the Camassa-Holm equation with dispersion is found. According to the linear structure, we obtain the superposition of multi-solutions to Camassa-Holm equation with dispersion.展开更多
The (G'/G, 1/G)-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the (G'/G)-expansion method proposed recently, is present...The (G'/G, 1/G)-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the (G'/G)-expansion method proposed recently, is presented. By using this method abundant travelling wave so- lutions with arbitrary parameters of the Zakharov equations are successfully obtained. When the parameters are replaced by special values, the well-known solitary wave solutions of the equations are rediscovered from the travelling waves.展开更多
A Riccati equation involving a parameter and symbolic computation are used to uniformly construct the different forms of travelling wave solutions for nonlinear evolution equations.It is shown that the sign of the pa...A Riccati equation involving a parameter and symbolic computation are used to uniformly construct the different forms of travelling wave solutions for nonlinear evolution equations.It is shown that the sign of the parameter can be applied in judging the existence of various forms of travelling wave solutions.An efficiency of this method is demonstrated on some equations,which include Burgers Huxley equation,Caudrey Dodd Gibbon Kawada equation,generalized Benjamin Bona Mahony equation and generalized Fisher equation.展开更多
In this paper, a new auxiliary equation method is used to find exact travelling wave solutions to the (1+1)-dimensional KdV equation. Some exact travelling wave solu- tions with parameters have been obtained, which...In this paper, a new auxiliary equation method is used to find exact travelling wave solutions to the (1+1)-dimensional KdV equation. Some exact travelling wave solu- tions with parameters have been obtained, which cover the existing solutions. Compared to other methods, the presented method is more direct, more concise, more effective, and easier for calculations. In addition, it can be used to solve other nonlinear evolution equations in mathematical physics.展开更多
In this paper, author considers a 3 x 3 system for a reacting flow model propesed by [9]. Since this model has source term, it can be considered as a relaxation approximation to 2 x 2 systems of conservation laws, whi...In this paper, author considers a 3 x 3 system for a reacting flow model propesed by [9]. Since this model has source term, it can be considered as a relaxation approximation to 2 x 2 systems of conservation laws, which include the well-known p-system. From this viewpoint, the author establishes the global existence and the nonlinear stability of travelling wave solutions by L-2 energy method.展开更多
This paper is concerned with the convergence rates to travelling waves for a relaxation model with general flux functions. Compared with former results in this direction, the main novelty in this paper lies in the fac...This paper is concerned with the convergence rates to travelling waves for a relaxation model with general flux functions. Compared with former results in this direction, the main novelty in this paper lies in the fact that the initial disturbance can be chosen large in suitable norm. Our analysis is based on the L^1-stability results obtained by C. Mascia and R. Natalini in [12].展开更多
By using plug flow and trajectory model, the elimination efficiency of the inclusions from liquid metals purified by travelling magnetic field (TMF) in either a triangle or a square pipe was analyzed theoretically. Th...By using plug flow and trajectory model, the elimination efficiency of the inclusions from liquid metals purified by travelling magnetic field (TMF) in either a triangle or a square pipe was analyzed theoretically. The ways to improve the elimination efficiency were suggested. The results using different kinds of pipes were reciprocally compared. It is determined that by means of TMF to eliminate inclusions the efficiency is affected by the diameter of the inclusions, in which the inclusions can be removed most efficiently, is optimized.展开更多
In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some e...In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.展开更多
Based on the beam wave synchronous interaction in transverse and longitudinal directions at the same time and starting from Maxwell’s equation and linear Vlasov equation, the beam–wave interaction ‘hot’ dispersion...Based on the beam wave synchronous interaction in transverse and longitudinal directions at the same time and starting from Maxwell’s equation and linear Vlasov equation, the beam–wave interaction ‘hot’ dispersion equation considering both cyclotron resonance and Cherenkov resonance in a staggered double metallic grating traveling wave tube is deduced.Through the reasonable selection for geometric and electrical parameters, the numerical calculation and analysis of the ‘hot’ dispersion equation shows that the beam–wave interaction gain and frequency band with the cyclotron resonance enhancement effect are higher than those with only Cherenkov resonance radiation.展开更多
The analysis approach of semi-active control for long-span rigid-continuous bridge under seismic travelling wave input is established. Magnetorheological dampers are set on the positions of the bridge beatings. The se...The analysis approach of semi-active control for long-span rigid-continuous bridge under seismic travelling wave input is established. Magnetorheological dampers are set on the positions of the bridge beatings. The semi-active control calculation and analysis are performed for a five-span rigid-continuous bridge under seismic travelling waves with different apparent surface velocities. The results indicate that travelling wave effect remarkably influences the uncontrolled seismic responses, the semi-active control seismic responses and vibration control effects for the long-span rigid-continuous bridge. It is disadvantageous to the responses of the beams and the piers under the travelling wave input with lower apparent surface velocity, and travelling wave effect can decrease the vibration control effects evidently. Therefore, the travelling wave effect should be considered for the selection of the parameter values of semi-active control system in order to get the designing control effect.展开更多
Based on the computerized symbolic computation, some new exact travelling wave solutions to three nonlinear evolution equations are explicitly obtained by replacing the tanhξ in tanh-function method with the solution...Based on the computerized symbolic computation, some new exact travelling wave solutions to three nonlinear evolution equations are explicitly obtained by replacing the tanhξ in tanh-function method with the solutions of a new auxiliary ordinary differential equation.展开更多
This article deals with waves in a circular cylindrical rod composed of a compressible Mooney Rivlin material. All kinds of travelling waves and the conditions for their existence are studied by using the method of ...This article deals with waves in a circular cylindrical rod composed of a compressible Mooney Rivlin material. All kinds of travelling waves and the conditions for their existence are studied by using the method of nonlinear dynamics.展开更多
文摘In this paper, we study the propagation and its failure to propagate (pinning) of a travelling wave in a Nagumo type equation, an equation that describes impulse propagation in nerve axons that also models population growth with Allee effect. An analytical solution is derived for the traveling wave and the work is extended to a discrete formulation with a piecewise linear reaction function. We propose an operator splitting numerical scheme to solve the equation and demonstrate that the wave either propagates or gets pinned based on how the spatial mesh is chosen.
文摘Travelling Salesman Problem(TSP)is a discrete hybrid optimization problem considered NP-hard.TSP aims to discover the shortest Hamilton route that visits each city precisely once and then returns to the starting point,making it the shortest route feasible.This paper employed a Farmland Fertility Algorithm(FFA)inspired by agricultural land fertility and a hyper-heuristic technique based on the Modified Choice Function(MCF).The neighborhood search operator can use this strategy to automatically select the best heuristic method formaking the best decision.Lin-Kernighan(LK)local search has been incorporated to increase the efficiency and performance of this suggested approach.71 TSPLIB datasets have been compared with different algorithms to prove the proposed algorithm’s performance and efficiency.Simulation results indicated that the proposed algorithm outperforms comparable methods of average mean computation time,average percentage deviation(PDav),and tour length.
文摘Using Genetic Algorithms (GAs) is a powerful tool to get solution to large scale design optimization problems. This paper used GA to solve complicated design optimization problems in two different applications. The aims are to implement the genetic algorithm to solve these two different (nested) problems, and to get the best or optimization solutions.
基金Supported by the NNSF of China(60464001) Guangxi Science Foundation(0575092).
文摘In this paper, the generalized Dodd-Bullough-Mikhailov equation is studied. The existence of periodic wave and unbounded wave solutions is proved by using the method of bifurcation theory of dynamical systems. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.Some exact explicit parametric representations of the above travelling solutions are obtained.
基金The work is supported by the National Natural Science Foundation of China and LASG.
文摘The scientific achievements of travelling waves in a barotropic atmosphere are introduced, including i) the existence conditions of periodic solutions (wavetrain solutions) and solitary wave solutions (pulse solutions), together with the solution finding methods and a series of related problems, ii) seeking solutions of monotonous wave (wave front) and of nonmonotonous travelling wave (oscillatory wave) by using phase plane shooting technique and hi) progress in the study of travelling wave solution at home and abroad. The investigation of travelling wave solutions in recent years has been found in mathematics, physics, chemistry, biology and other sciences. Over the past decade the problem has been the subject of much interest and become an important area of research. So it is no doubt of great significance to investigate the travelling wave solutions and thereby explain phenomena of weather.
文摘The travelling wave solutions (TWS) in a class of P. D. E. is studied. The travelling wave equation of this P. D. E. is a planar cubic polynomial system in three-parameter space. The study for M became the topological classifications of bifurcations of phase portraits defined by the planar system. B using the theory of planar dynamical systems to do qualitative analysis, all topological classifications of the cubic polynomial system can be obtained. Returning the results of the phase plane analysis to TWS, u(xi), and considering discontinuity of the right side of the equation of TWS when xi = x - ct is varied along a phase orbit and passing through a singular curve, all conditions of existence of smooth and nonsmooth travelling waves are given.
文摘A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a (1+1)-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems.
基金Supported by the National Natural Sciences Foundation of China(40676016 and 10471039)the National Key Project for Basic Research(2003CB415101-03 and 2004CB418304)+2 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)in part by E-Institutes of Shanghai Municipal Education Commission(N.E03004)the Natural Science Foundation of Zeijiang,China(Y606268).
文摘In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.
文摘Under the travelling wave transformation, the Camassa-Holm equation with dispersion is reduced to an integrable ordinary differential equation (ODE), whose general solution can be obtained using the trick of one-parameter group. Furthermore, by using a complete discrimination system for polynomial, the classification of all single travelling wave solutions to the Camassa-Holm equation with dispersion is obtained. In particular, an affine subspace structure in the set of the solutions of the reduced ODE is obtained. More generally, an implicit linear structure in the Camassa-Holm equation with dispersion is found. According to the linear structure, we obtain the superposition of multi-solutions to Camassa-Holm equation with dispersion.
基金Supported by the International Cooperation and Exchanges Foundation of Henan Province (084300510060)the Youth Science Foundation of Henan University of Science and Technology of China (2008QN026)
文摘The (G'/G, 1/G)-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the (G'/G)-expansion method proposed recently, is presented. By using this method abundant travelling wave so- lutions with arbitrary parameters of the Zakharov equations are successfully obtained. When the parameters are replaced by special values, the well-known solitary wave solutions of the equations are rediscovered from the travelling waves.
基金Supported by the Postdoctoral Science Foundation of ChinaChinese Basic Research Plan"MathematicsMechanization and A Platform
文摘A Riccati equation involving a parameter and symbolic computation are used to uniformly construct the different forms of travelling wave solutions for nonlinear evolution equations.It is shown that the sign of the parameter can be applied in judging the existence of various forms of travelling wave solutions.An efficiency of this method is demonstrated on some equations,which include Burgers Huxley equation,Caudrey Dodd Gibbon Kawada equation,generalized Benjamin Bona Mahony equation and generalized Fisher equation.
基金supported by the National Natural Science Foundation of China (No.10461005)the Ph.D.Programs Foundation of Ministry of Education of China (No.20070128001)the High Education Science Research Program of Inner Mongolia (No.NJZY08057)
文摘In this paper, a new auxiliary equation method is used to find exact travelling wave solutions to the (1+1)-dimensional KdV equation. Some exact travelling wave solu- tions with parameters have been obtained, which cover the existing solutions. Compared to other methods, the presented method is more direct, more concise, more effective, and easier for calculations. In addition, it can be used to solve other nonlinear evolution equations in mathematical physics.
文摘In this paper, author considers a 3 x 3 system for a reacting flow model propesed by [9]. Since this model has source term, it can be considered as a relaxation approximation to 2 x 2 systems of conservation laws, which include the well-known p-system. From this viewpoint, the author establishes the global existence and the nonlinear stability of travelling wave solutions by L-2 energy method.
基金The subject is supported by National Natural Sciences Foundation of China(10001036)
文摘This paper is concerned with the convergence rates to travelling waves for a relaxation model with general flux functions. Compared with former results in this direction, the main novelty in this paper lies in the fact that the initial disturbance can be chosen large in suitable norm. Our analysis is based on the L^1-stability results obtained by C. Mascia and R. Natalini in [12].
文摘By using plug flow and trajectory model, the elimination efficiency of the inclusions from liquid metals purified by travelling magnetic field (TMF) in either a triangle or a square pipe was analyzed theoretically. The ways to improve the elimination efficiency were suggested. The results using different kinds of pipes were reciprocally compared. It is determined that by means of TMF to eliminate inclusions the efficiency is affected by the diameter of the inclusions, in which the inclusions can be removed most efficiently, is optimized.
基金supported by the Research Foundation of Education Bureau of Hubei Province,China (Grant No Z200612001)the Natural Science Foundation of Yangtze University (Grant No 20061222)
文摘In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.
基金supported by National Natural Science Foundation of China(No.61671431)
文摘Based on the beam wave synchronous interaction in transverse and longitudinal directions at the same time and starting from Maxwell’s equation and linear Vlasov equation, the beam–wave interaction ‘hot’ dispersion equation considering both cyclotron resonance and Cherenkov resonance in a staggered double metallic grating traveling wave tube is deduced.Through the reasonable selection for geometric and electrical parameters, the numerical calculation and analysis of the ‘hot’ dispersion equation shows that the beam–wave interaction gain and frequency band with the cyclotron resonance enhancement effect are higher than those with only Cherenkov resonance radiation.
基金National Natural Science Foundation of China (50439030)
文摘The analysis approach of semi-active control for long-span rigid-continuous bridge under seismic travelling wave input is established. Magnetorheological dampers are set on the positions of the bridge beatings. The semi-active control calculation and analysis are performed for a five-span rigid-continuous bridge under seismic travelling waves with different apparent surface velocities. The results indicate that travelling wave effect remarkably influences the uncontrolled seismic responses, the semi-active control seismic responses and vibration control effects for the long-span rigid-continuous bridge. It is disadvantageous to the responses of the beams and the piers under the travelling wave input with lower apparent surface velocity, and travelling wave effect can decrease the vibration control effects evidently. Therefore, the travelling wave effect should be considered for the selection of the parameter values of semi-active control system in order to get the designing control effect.
基金Supported by the Natural Science Foundation and the High Education Science Research ProgramNJ0 2 0 35 of Inner Mongoli
文摘Based on the computerized symbolic computation, some new exact travelling wave solutions to three nonlinear evolution equations are explicitly obtained by replacing the tanhξ in tanh-function method with the solutions of a new auxiliary ordinary differential equation.
文摘This article deals with waves in a circular cylindrical rod composed of a compressible Mooney Rivlin material. All kinds of travelling waves and the conditions for their existence are studied by using the method of nonlinear dynamics.