The qualitative theory of differential equations is applied to the Ostrovsky equation. The cusped soliton and loop-soliton solutions of the Ostrovsky equation are obtained. Asymptotic behavior of eusped soliton soluti...The qualitative theory of differential equations is applied to the Ostrovsky equation. The cusped soliton and loop-soliton solutions of the Ostrovsky equation are obtained. Asymptotic behavior of eusped soliton solutions is given. Numerical simulations are provided for cusped solitons and so-called loop-solitons of the Ostrovsky equation.展开更多
We investigate the refined Carleson’s problem of the free Ostrovsky equation{ut+■_(z)^(3)u+■_(x)^(-1)u=0,u(x,0)=f(x)where(x,t)∈R×R and f∈H^(s)(R).We illustrate the Hausdorff dimension of the divergence set f...We investigate the refined Carleson’s problem of the free Ostrovsky equation{ut+■_(z)^(3)u+■_(x)^(-1)u=0,u(x,0)=f(x)where(x,t)∈R×R and f∈H^(s)(R).We illustrate the Hausdorff dimension of the divergence set for the Ostrovsky equationα1,U(s)=1-2 s,1/4≤s≤1/2.展开更多
In this work, the Exp-function method is employed to find new wave solutions for the Sine-Gordon and Ostrovsky equation. The equations are simplified to the nonlinear partial differential equations and then different ...In this work, the Exp-function method is employed to find new wave solutions for the Sine-Gordon and Ostrovsky equation. The equations are simplified to the nonlinear partial differential equations and then different types of exact solutions are extracted by this method. It is shown that the Exp-function method is a powerful analytical method for solving other nonlinear equations occurring in nonlinear physical phenomena. Results are presented in contour plots that show the different values of effective parameters on the velocity profiles.展开更多
By the method of dynamical system, we construct the exact travelling wave solu- tions of a new Hamiltonian amplitude equation and the Ostrovsky equation. Based on this method, the new exact travelling wave solutions o...By the method of dynamical system, we construct the exact travelling wave solu- tions of a new Hamiltonian amplitude equation and the Ostrovsky equation. Based on this method, the new exact travelling wave solutions of the new Hamiltonian am- plitude equation and the Ostrovsky equation, such as solitary wave solutions, kink and anti-kink wave solutions and periodic travelling wave solutions, are obtained, respectively.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Supported by the National Natural Science Foundation of China under Grant Nos.10961011 and 60964006
文摘The qualitative theory of differential equations is applied to the Ostrovsky equation. The cusped soliton and loop-soliton solutions of the Ostrovsky equation are obtained. Asymptotic behavior of eusped soliton solutions is given. Numerical simulations are provided for cusped solitons and so-called loop-solitons of the Ostrovsky equation.
基金supported by the National Natural Science Foundation of China(11571118,11401180 and 11971356)。
文摘We investigate the refined Carleson’s problem of the free Ostrovsky equation{ut+■_(z)^(3)u+■_(x)^(-1)u=0,u(x,0)=f(x)where(x,t)∈R×R and f∈H^(s)(R).We illustrate the Hausdorff dimension of the divergence set for the Ostrovsky equationα1,U(s)=1-2 s,1/4≤s≤1/2.
文摘In this work, the Exp-function method is employed to find new wave solutions for the Sine-Gordon and Ostrovsky equation. The equations are simplified to the nonlinear partial differential equations and then different types of exact solutions are extracted by this method. It is shown that the Exp-function method is a powerful analytical method for solving other nonlinear equations occurring in nonlinear physical phenomena. Results are presented in contour plots that show the different values of effective parameters on the velocity profiles.
文摘By the method of dynamical system, we construct the exact travelling wave solu- tions of a new Hamiltonian amplitude equation and the Ostrovsky equation. Based on this method, the new exact travelling wave solutions of the new Hamiltonian am- plitude equation and the Ostrovsky equation, such as solitary wave solutions, kink and anti-kink wave solutions and periodic travelling wave solutions, are obtained, respectively.
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.
