By using the modified mapping method, we find new exact solutions of the Petviashvili equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function so...By using the modified mapping method, we find new exact solutions of the Petviashvili equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.展开更多
In this paper,dependent and independent variable transformations are introduced to solve the Degasperis-Procesi equation.It is shown that different kinds of solutions can be obtained to the Degasperis-Procesi equation.
In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for three nonlinear differential-difference equations are obtained.
Using Jacobi elliptic function linear superposition approach for the (1+1)-dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) equation and the (2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) equation, many ne...Using Jacobi elliptic function linear superposition approach for the (1+1)-dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) equation and the (2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) equation, many new periodic travelling wave solutions with different periods and velocities are obtained based on the known periodic solutions. This procedure is crucially dependent on a sequence of cyclic identities involving Jacobi elliptic functions sn(), cn(), and dn().展开更多
The generalized maximum principle of Lou and Ni is extended from elliptic equations to parabolic equations. By this result, one can show that the system of fugal mycelia has a global attractor if the diffusion coeffic...The generalized maximum principle of Lou and Ni is extended from elliptic equations to parabolic equations. By this result, one can show that the system of fugal mycelia has a global attractor if the diffusion coefficient D = 0 and the solution blows up ifD= 0. The method of linearization is applied to derive the existence of Hopfs bifurcation which is the signature of instability of Turing system. The increasing of the size of the attractor and the existence of Hopf＇ s bifurcation indicate that there is a threshold that initiates the instability.展开更多
The two-dimensional flows around a cylinder between two parallel walls at Re=40 and Re=100 are simulated with computational fluid dynamics(CFD). The governing equations are Navier-Stokes equations. They are discretize...The two-dimensional flows around a cylinder between two parallel walls at Re=40 and Re=100 are simulated with computational fluid dynamics(CFD). The governing equations are Navier-Stokes equations. They are discretized with finite volume method(FVM) and the solution is iterated with PISO Algorithm. Then, the calculating results are compared with the numerical results in literature, and good agreements are obtained. After that, the mechanism of the formation of Karman vortex street is investigated and the instability of the entire flow field is analyzed with the energy gradient theory. It is found that the two eddies attached at the rear of the cylinder have no effect on the flow instability for steady flow, i.e., they don't contribute to the formation of Karman vortex street. The formation of Karman vortex street originates from the combinations of the interaction of two shear layers at two lateral sides of the cylinder and the absolute instability in the cylinder wake. For the flow with Karman vortex street, the initial instability occurs at the region in a vortex downstream of the wake and the center of a vortex firstly loses its stability in a vortex. For pressure driven flow, it is confirmed that the inflection point on the time-averaged velocity profile leads to the instability. It is concluded that the energy gradient theory is potentially applicable to study the flow stability and to reveal the mechanism of turbulent transition.展开更多
This paper considers the mixed covolume method for the second-order elliptic equations over quadrilaterals.Superconvergence results are established in this paper on quadrilateral grids satisfying the h^2-parallelogram...This paper considers the mixed covolume method for the second-order elliptic equations over quadrilaterals.Superconvergence results are established in this paper on quadrilateral grids satisfying the h^2-parallelogram condition when the lowest-order Raviart-Thomas space is employed in the mixed covolume method.The authors prove O(h^2) accuracy between the approximate velocity or pressure and a suitable projection of the real velocity or pressure in the L^2 norm.Numerical experiments illustrating the theoretical results are provided.展开更多
基金the State Key Basic Research Program of China under Grant No.2004CB418304
文摘By using the modified mapping method, we find new exact solutions of the Petviashvili equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.
基金National Natural Science Foundation of China under Grant Nos.40775040 and 90511009
文摘In this paper,dependent and independent variable transformations are introduced to solve the Degasperis-Procesi equation.It is shown that different kinds of solutions can be obtained to the Degasperis-Procesi equation.
基金The project supported by National Natural Science Foundation of China under Grant Nos.90511009 and 40305006
文摘In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for three nonlinear differential-difference equations are obtained.
文摘Using Jacobi elliptic function linear superposition approach for the (1+1)-dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) equation and the (2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) equation, many new periodic travelling wave solutions with different periods and velocities are obtained based on the known periodic solutions. This procedure is crucially dependent on a sequence of cyclic identities involving Jacobi elliptic functions sn(), cn(), and dn().
文摘The generalized maximum principle of Lou and Ni is extended from elliptic equations to parabolic equations. By this result, one can show that the system of fugal mycelia has a global attractor if the diffusion coefficient D = 0 and the solution blows up ifD= 0. The method of linearization is applied to derive the existence of Hopfs bifurcation which is the signature of instability of Turing system. The increasing of the size of the attractor and the existence of Hopf＇ s bifurcation indicate that there is a threshold that initiates the instability.
基金supported by the Natural Science Foundation of Zhejiang Province LY14E060003 )the Special Major Project of Science and Technology of Zhejiang Province (No.2013C01139)+1 种基金Zhejiang Province Key Science and Technology Innovation Team (2 013TD18)the Science Foundation of Zhejiang Sci-Tech University (No.11130032661215)
文摘The two-dimensional flows around a cylinder between two parallel walls at Re=40 and Re=100 are simulated with computational fluid dynamics(CFD). The governing equations are Navier-Stokes equations. They are discretized with finite volume method(FVM) and the solution is iterated with PISO Algorithm. Then, the calculating results are compared with the numerical results in literature, and good agreements are obtained. After that, the mechanism of the formation of Karman vortex street is investigated and the instability of the entire flow field is analyzed with the energy gradient theory. It is found that the two eddies attached at the rear of the cylinder have no effect on the flow instability for steady flow, i.e., they don't contribute to the formation of Karman vortex street. The formation of Karman vortex street originates from the combinations of the interaction of two shear layers at two lateral sides of the cylinder and the absolute instability in the cylinder wake. For the flow with Karman vortex street, the initial instability occurs at the region in a vortex downstream of the wake and the center of a vortex firstly loses its stability in a vortex. For pressure driven flow, it is confirmed that the inflection point on the time-averaged velocity profile leads to the instability. It is concluded that the energy gradient theory is potentially applicable to study the flow stability and to reveal the mechanism of turbulent transition.
基金supported by the '985' program of Jilin Universitythe National Natural Science Foundation of China under Grant No.10971082the NSAF of China under Grant No.11076014
文摘This paper considers the mixed covolume method for the second-order elliptic equations over quadrilaterals.Superconvergence results are established in this paper on quadrilateral grids satisfying the h^2-parallelogram condition when the lowest-order Raviart-Thomas space is employed in the mixed covolume method.The authors prove O(h^2) accuracy between the approximate velocity or pressure and a suitable projection of the real velocity or pressure in the L^2 norm.Numerical experiments illustrating the theoretical results are provided.
