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
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.
