Much effort has been devoted to researching the common Rosenau equation, but the numerical method of it has not been studied. In this paper, a conservative Crank-Nicolson difference scheme for an initial-boundary valu...Much effort has been devoted to researching the common Rosenau equation, but the numerical method of it has not been studied. In this paper, a conservative Crank-Nicolson difference scheme for an initial-boundary value problem of the generalized Rosenau equation is proposed. Existence and uniqueness of numerical solutions are derived. By method of discrete energy, the second order convergence and stability are discussed. Numerical examples demonstrate the theoretical results.展开更多
In this work, we study the generalized Rosenau-KdV equation. We shall use the sech-ansatze method to derive the solitary wave solutions of this equation.
This paper considers the Rosenau equation with a moving control δtu＋δtδx4u＋δxu＋uδzu=a（x＋ct）h（x,t）,c≠0,x∈T=R/（2πZ）,t〉0, The authors prove that the Rosenau equation with a moving control is locally ex...This paper considers the Rosenau equation with a moving control δtu＋δtδx4u＋δxu＋uδzu=a（x＋ct）h（x,t）,c≠0,x∈T=R/（2πZ）,t〉0, The authors prove that the Rosenau equation with a moving control is locally exact controllable in H8（T） with s ≥ 0 and globally exponential stable in H8（T） with s ≥2. The two results nontrivially extend the work of （Rosier L and Zhang B Y, 2013） from the BBM equation to the Rosenau equation.展开更多
Under investigation in this paper is the invariance properties of the time fractional Rosenau-Haynam equation, which can be used to describe the formation of patterns in liquid drops. By using the Lie group analysis m...Under investigation in this paper is the invariance properties of the time fractional Rosenau-Haynam equation, which can be used to describe the formation of patterns in liquid drops. By using the Lie group analysis method, the vector fields and symmetry reductions of the equation are derived, respectively. Moreover, based on the power series theory, a kind of explicit power series solutions for the equation are well constructed with a detailed derivation. Finally, by using the new conservation theorem, two kinds of conservation laws of the equation are well constructed with a detailed derivation.展开更多
基金The National Natural Science Foundation of China (No.40701014)the Scientific Research Fund of Sichuan Provincial Education Department (No.09ZB081)the Research Fund of key Discipline of Xihua University:Applied Mathe-matics (No.XZD0910-09-1)
文摘Much effort has been devoted to researching the common Rosenau equation, but the numerical method of it has not been studied. In this paper, a conservative Crank-Nicolson difference scheme for an initial-boundary value problem of the generalized Rosenau equation is proposed. Existence and uniqueness of numerical solutions are derived. By method of discrete energy, the second order convergence and stability are discussed. Numerical examples demonstrate the theoretical results.
文摘In this work, we study the generalized Rosenau-KdV equation. We shall use the sech-ansatze method to derive the solitary wave solutions of this equation.
基金supported by China Postdoctoral Science Foundation under Grant No.2016M592634Chongqing Postdoctoral Science Special Foundation under Grant No.Xm2016035the National Natural Science Foundation of China under Grant Nos.11371384 and 11571244
文摘This paper considers the Rosenau equation with a moving control δtu＋δtδx4u＋δxu＋uδzu=a（x＋ct）h（x,t）,c≠0,x∈T=R/（2πZ）,t〉0, The authors prove that the Rosenau equation with a moving control is locally exact controllable in H8（T） with s ≥ 0 and globally exponential stable in H8（T） with s ≥2. The two results nontrivially extend the work of （Rosier L and Zhang B Y, 2013） from the BBM equation to the Rosenau equation.
基金Supported by the Fundamental Research Fund for Talents Cultivation Project of the China University of Mining and Technology under Grant No.YC150003
文摘Under investigation in this paper is the invariance properties of the time fractional Rosenau-Haynam equation, which can be used to describe the formation of patterns in liquid drops. By using the Lie group analysis method, the vector fields and symmetry reductions of the equation are derived, respectively. Moreover, based on the power series theory, a kind of explicit power series solutions for the equation are well constructed with a detailed derivation. Finally, by using the new conservation theorem, two kinds of conservation laws of the equation are well constructed with a detailed derivation.
