The global fast dynamics for the generalized symmetric regularized long wave equation with damping term is considered. The squeezing property of the nonlinear semi_group associated with this equation and the existence...The global fast dynamics for the generalized symmetric regularized long wave equation with damping term is considered. The squeezing property of the nonlinear semi_group associated with this equation and the existence of exponential attractor are proved. The upper bounds of its fractal dimension are also estimated.展开更多
Abstract In the present paper, we construct two approximate inertial manifolds for the generalized symmetric regularized long wave equations with damping term. The orders of approximations of these manifolds to the gl...Abstract In the present paper, we construct two approximate inertial manifolds for the generalized symmetric regularized long wave equations with damping term. The orders of approximations of these manifolds to the global attractor are derived.展开更多
The existence and uniqueness of the global smooth solution to the initial-boundary valueproblem of a system of multi-dimensions SRWE are proved. The sufficient conditions of 'blowingup' of the solution are given.
This paper deals with the asymptotic behaviour of solutions for thegeneralized symmetric regularized long wave equations with dissipation term. We first show theexistence of global weak attractors for the periodic ini...This paper deals with the asymptotic behaviour of solutions for thegeneralized symmetric regularized long wave equations with dissipation term. We first show theexistence of global weak attractors for the periodic initial value problem of this equations in H^2x H^1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the globalweak attractor is actually the global strong attractor for S(t) in H^2 (Ω) x H^1 (Ω). The finitedimensionality of the global attractor is also established.展开更多
An efficient and accurate exponential wave integrator Fourier pseudospectral （EWI-FP） method is proposed and analyzed for solving the symmetric regularized-long-wave （SRLW） equation, which is used for modeling the...An efficient and accurate exponential wave integrator Fourier pseudospectral （EWI-FP） method is proposed and analyzed for solving the symmetric regularized-long-wave （SRLW） equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseudospectral method for spatial discretization. The scheme is fully explicit and efficient due to the fast Fourier transform. Numerical analysis of the proposed EWI-FP method is carried out and rigorous error estimates are established without CFL-type condition by means of the mathematical induction. The error bound shows that EWI-FP has second order accuracy in time and spectral accuracy in space. Numerical results are reported to confirm the theoretical studies and indicate that the error bound here is optimal.展开更多
In this paper, we investigate the space-time fractional symmetric regularized long wave equation. By using the Backlund transformations and nonlinear superposition formulas of solutions to Riccati equation, we present...In this paper, we investigate the space-time fractional symmetric regularized long wave equation. By using the Backlund transformations and nonlinear superposition formulas of solutions to Riccati equation, we present infinite sequence solutions for space-time fractional symmetric regularized long wave equation. This method can be extended to solve other nonlinear fractional partial differential equations.展开更多
A graph is symmetric or 1-regular if its automorphism group is transitive or regular on the arc set of the graph, respectively. We classify the connected pentavalent symmetric graphs of order 2p^3 for each prime p. Al...A graph is symmetric or 1-regular if its automorphism group is transitive or regular on the arc set of the graph, respectively. We classify the connected pentavalent symmetric graphs of order 2p^3 for each prime p. All those symmetric graphs appear as normal Cayley graphs on some groups of order 2p^3 and their automorphism groups are determined. For p = 3, no connected pentavalent symmetric graphs of order 2p^3 exist. However, for p = 2 or 5, such symmetric graph exists uniquely in each case. For p 7, the connected pentavalent symmetric graphs of order 2p^3 are all regular covers of the dipole Dip5 with covering transposition groups of order p^3, and they consist of seven infinite families; six of them are 1-regular and exist if and only if 5 |(p- 1), while the other one is 1-transitive but not 1-regular and exists if and only if 5 |(p ± 1). In the seven infinite families, each graph is unique for a given order.展开更多
In this study,we implement the generalized(G/G)-expansion method established by Wang et al.to examine wave solutions to some nonlinear evolution equations.The method,known as the double(G/G,1/G)-expansion method is ...In this study,we implement the generalized(G/G)-expansion method established by Wang et al.to examine wave solutions to some nonlinear evolution equations.The method,known as the double(G/G,1/G)-expansion method is used to establish abundant new and further general exact wave solutions to the(3+1)-dimensional Jimbo-Miwa equation,the(3+1)-dimensional Kadomtsev-Petviashvili equation and symmetric regularized long wave equation.The solutions are extracted in terms of hyperbolic function,trigonometric function and rational function.The solitary wave solutions are constructed from the obtained traveling wave solutions if the parameters received some definite values.Graphs of the solutions are also depicted to describe the phenomena apparently and the shapes of the obtained solutions are singular periodic,anti-kink,singular soliton,singular anti-bell shape,compaction etc.This method is straightforward,compact and reliable and gives huge new closed form traveling wave solutions of nonlinear evolution equations in ocean engineering.展开更多
In this study,the authors obtained the soliton and periodic wave solutions for time fractional symmetric regularized long wave equation(SRLW)and Ostrovsky equation(OE)both arising as a model in ocean engineering.For t...In this study,the authors obtained the soliton and periodic wave solutions for time fractional symmetric regularized long wave equation(SRLW)and Ostrovsky equation(OE)both arising as a model in ocean engineering.For this aim modified extended tanh-function(mETF)is used.While using this method,chain rule is employed to turn fractional nonlinear partial differential equation into the nonlinear ordinary differential equation in integer order.Owing to the chain rule,there is no further requirement for any normalization or discretization.Beta derivative which involves fractional term is used in considered mathematical models.Obtaining the exact solutions of these equations is very important for knowing the wave behavior in ocean engineering models.展开更多
基金ProjectsupportedbytheNationalNaturalScienceFoundationofChina (No .1 0 2 71 0 3 4)
文摘The global fast dynamics for the generalized symmetric regularized long wave equation with damping term is considered. The squeezing property of the nonlinear semi_group associated with this equation and the existence of exponential attractor are proved. The upper bounds of its fractal dimension are also estimated.
文摘Abstract In the present paper, we construct two approximate inertial manifolds for the generalized symmetric regularized long wave equations with damping term. The orders of approximations of these manifolds to the global attractor are derived.
文摘The existence and uniqueness of the global smooth solution to the initial-boundary valueproblem of a system of multi-dimensions SRWE are proved. The sufficient conditions of 'blowingup' of the solution are given.
基金This research is supported by the National Natural Science Foundation of China(Grant 10271034).
文摘This paper deals with the asymptotic behaviour of solutions for thegeneralized symmetric regularized long wave equations with dissipation term. We first show theexistence of global weak attractors for the periodic initial value problem of this equations in H^2x H^1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the globalweak attractor is actually the global strong attractor for S(t) in H^2 (Ω) x H^1 (Ω). The finitedimensionality of the global attractor is also established.
文摘An efficient and accurate exponential wave integrator Fourier pseudospectral （EWI-FP） method is proposed and analyzed for solving the symmetric regularized-long-wave （SRLW） equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseudospectral method for spatial discretization. The scheme is fully explicit and efficient due to the fast Fourier transform. Numerical analysis of the proposed EWI-FP method is carried out and rigorous error estimates are established without CFL-type condition by means of the mathematical induction. The error bound shows that EWI-FP has second order accuracy in time and spectral accuracy in space. Numerical results are reported to confirm the theoretical studies and indicate that the error bound here is optimal.
基金Acknowledgments This work is supported by the National Natural Science Foundation of China （Grant No. 11462019） and the Scientific Research Foundation of Inner Mongolia University for Nationalities （Grant No. NMD1306）. The author would like to thank the referees for their time and comments.
文摘In this paper, we investigate the space-time fractional symmetric regularized long wave equation. By using the Backlund transformations and nonlinear superposition formulas of solutions to Riccati equation, we present infinite sequence solutions for space-time fractional symmetric regularized long wave equation. This method can be extended to solve other nonlinear fractional partial differential equations.
基金supported by National Natural Science Foundation of China (Grant Nos. 11571035 and 11231008)
文摘A graph is symmetric or 1-regular if its automorphism group is transitive or regular on the arc set of the graph, respectively. We classify the connected pentavalent symmetric graphs of order 2p^3 for each prime p. All those symmetric graphs appear as normal Cayley graphs on some groups of order 2p^3 and their automorphism groups are determined. For p = 3, no connected pentavalent symmetric graphs of order 2p^3 exist. However, for p = 2 or 5, such symmetric graph exists uniquely in each case. For p 7, the connected pentavalent symmetric graphs of order 2p^3 are all regular covers of the dipole Dip5 with covering transposition groups of order p^3, and they consist of seven infinite families; six of them are 1-regular and exist if and only if 5 |(p- 1), while the other one is 1-transitive but not 1-regular and exists if and only if 5 |(p ± 1). In the seven infinite families, each graph is unique for a given order.
文摘In this study,we implement the generalized(G/G)-expansion method established by Wang et al.to examine wave solutions to some nonlinear evolution equations.The method,known as the double(G/G,1/G)-expansion method is used to establish abundant new and further general exact wave solutions to the(3+1)-dimensional Jimbo-Miwa equation,the(3+1)-dimensional Kadomtsev-Petviashvili equation and symmetric regularized long wave equation.The solutions are extracted in terms of hyperbolic function,trigonometric function and rational function.The solitary wave solutions are constructed from the obtained traveling wave solutions if the parameters received some definite values.Graphs of the solutions are also depicted to describe the phenomena apparently and the shapes of the obtained solutions are singular periodic,anti-kink,singular soliton,singular anti-bell shape,compaction etc.This method is straightforward,compact and reliable and gives huge new closed form traveling wave solutions of nonlinear evolution equations in ocean engineering.
文摘In this study,the authors obtained the soliton and periodic wave solutions for time fractional symmetric regularized long wave equation(SRLW)and Ostrovsky equation(OE)both arising as a model in ocean engineering.For this aim modified extended tanh-function(mETF)is used.While using this method,chain rule is employed to turn fractional nonlinear partial differential equation into the nonlinear ordinary differential equation in integer order.Owing to the chain rule,there is no further requirement for any normalization or discretization.Beta derivative which involves fractional term is used in considered mathematical models.Obtaining the exact solutions of these equations is very important for knowing the wave behavior in ocean engineering models.
