A new three-component Camassa-Holm equation is introduced. This system is endowed with a structuresimilar to the Camassa-Holm equation. It has peakon solitons and conserves H^1-norm conservation law.
It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are ...It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are directly constructed. In addition, a class of nonlocal symmetries depending on the pseudo-potentials are obtained.展开更多
With Arena strawberry as experimental materials, heat treatments combined with shoot tip culture were used to explore their detoxification effects. The results indicated that if not heated, splitting shoot tips direct...With Arena strawberry as experimental materials, heat treatments combined with shoot tip culture were used to explore their detoxification effects. The results indicated that if not heated, splitting shoot tips directly could not completely remove viruses. On the other hand, it will be obviously improved after shoot tips are heated. Incubators heat treatment （inconstant temperature） with shoot tip culture, constant temperature water bath incubation process with meristem-tip culture, hot air treatment （constant temperature） with apical meristem culture were three methods tested in searching for virus-free of Arena strawberry in this experiment. And their virus-free rates were 78.9%, 86.0% and 50.0% respectively. Of the three methods, the second, constant temperature water bath process with shoot tip culture, with 78.7% survival, is the best. Thus, it can be inferred that constant temperature water bath treatment combined with shoot tip culture might be the most appropriate method to remove viruses of Arena strawberry.展开更多
Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite differ...Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations.Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.展开更多
The generalized fractional Burgers equation is studied in this paper. Using the classical Lie symmetry method, all of the vector fields and symmetry reduction of the equation with nonlinearity are constructed. In part...The generalized fractional Burgers equation is studied in this paper. Using the classical Lie symmetry method, all of the vector fields and symmetry reduction of the equation with nonlinearity are constructed. In particular, an exact solution ＆ provided by using the ansatz method. In addition, other types of exact solution are obtained via the invariant subspace method. Finally, conservation laws for this equation are derived.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos. 10671156 and 10671153
文摘A new three-component Camassa-Holm equation is introduced. This system is endowed with a structuresimilar to the Camassa-Holm equation. It has peakon solitons and conserves H^1-norm conservation law.
基金Supported by the China NSF for Distinguished Young Scholars under Grant No.10925104
文摘It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are directly constructed. In addition, a class of nonlocal symmetries depending on the pseudo-potentials are obtained.
文摘With Arena strawberry as experimental materials, heat treatments combined with shoot tip culture were used to explore their detoxification effects. The results indicated that if not heated, splitting shoot tips directly could not completely remove viruses. On the other hand, it will be obviously improved after shoot tips are heated. Incubators heat treatment （inconstant temperature） with shoot tip culture, constant temperature water bath incubation process with meristem-tip culture, hot air treatment （constant temperature） with apical meristem culture were three methods tested in searching for virus-free of Arena strawberry in this experiment. And their virus-free rates were 78.9%, 86.0% and 50.0% respectively. Of the three methods, the second, constant temperature water bath process with shoot tip culture, with 78.7% survival, is the best. Thus, it can be inferred that constant temperature water bath treatment combined with shoot tip culture might be the most appropriate method to remove viruses of Arena strawberry.
基金Supported by the National Natural Science Foundation of China under Grant No.91130013Hunan Provincial Innovation Foundation under Grant No.CX2012B010+1 种基金the Innovation Fund of National University of Defense Technology under Grant No.B120205the Open Foundation of State Key Laboratory
文摘Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations.Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.
文摘The generalized fractional Burgers equation is studied in this paper. Using the classical Lie symmetry method, all of the vector fields and symmetry reduction of the equation with nonlinearity are constructed. In particular, an exact solution ＆ provided by using the ansatz method. In addition, other types of exact solution are obtained via the invariant subspace method. Finally, conservation laws for this equation are derived.
