Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2...Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.展开更多
The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich e...The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich explicit and exact travelling wave solutions,which contain solitary-wave solutions,periodic solutions,and combined formal solitary-wave solutions,are obtained.展开更多
The mechanical effects of bolt-mesh-anchor coupling support in deep tunnels were studied by using a numerical method, based on deep tunnel coupling supporting techniques and non-linear deformation mechanical theory of...The mechanical effects of bolt-mesh-anchor coupling support in deep tunnels were studied by using a numerical method, based on deep tunnel coupling supporting techniques and non-linear deformation mechanical theory of rock mass at great depths.It is shown that the potential of a rigid bolt support can be efficiently activated through the coupling effect between a bolt-net support and the surrounding rock.It is found that the accumulated plastic energy in the surrounding rock can be sufficiently transformed by the coupling effect of a bolt-mesh-tray support.The strength of the surrounding rock mass can be mobilized to control the deforma-tion of the surrounding rock by a pre-stress and time-space effect of the anchor support.The high stress transformation effect can be realized by the mechanical coupling effect of the bolt-mesh-anchor support, whereby the force of the support and deformation of the surrounding rock tends to become uniform, leading to a sustained stability of the tunnel.展开更多
The multi-linear variable separation approach method is very useful to solve (2+1)-dimensional integrable systems. In this letter, we extend this method to solve (1+1)-dimensional Boiti system, (2+1)-dimensional Burge...The multi-linear variable separation approach method is very useful to solve (2+1)-dimensional integrable systems. In this letter, we extend this method to solve (1+1)-dimensional Boiti system, (2+1)-dimensional Burgers system, (2+1)-dimensional breaking soliton system, and (2+1)-dimensional Maccari system. Some new exact solutions are obtained and the universal formula obtained from many (2+1)-dimensional systems is extended or modified.展开更多
文摘Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.
文摘The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich explicit and exact travelling wave solutions,which contain solitary-wave solutions,periodic solutions,and combined formal solitary-wave solutions,are obtained.
基金Projects 2006CB202200 supported by the National Basic Research Program of ChinaNCET07-0800 by the Program for New Century Excellent Talents in Universities
文摘The mechanical effects of bolt-mesh-anchor coupling support in deep tunnels were studied by using a numerical method, based on deep tunnel coupling supporting techniques and non-linear deformation mechanical theory of rock mass at great depths.It is shown that the potential of a rigid bolt support can be efficiently activated through the coupling effect between a bolt-net support and the surrounding rock.It is found that the accumulated plastic energy in the surrounding rock can be sufficiently transformed by the coupling effect of a bolt-mesh-tray support.The strength of the surrounding rock mass can be mobilized to control the deforma-tion of the surrounding rock by a pre-stress and time-space effect of the anchor support.The high stress transformation effect can be realized by the mechanical coupling effect of the bolt-mesh-anchor support, whereby the force of the support and deformation of the surrounding rock tends to become uniform, leading to a sustained stability of the tunnel.
文摘The multi-linear variable separation approach method is very useful to solve (2+1)-dimensional integrable systems. In this letter, we extend this method to solve (1+1)-dimensional Boiti system, (2+1)-dimensional Burgers system, (2+1)-dimensional breaking soliton system, and (2+1)-dimensional Maccari system. Some new exact solutions are obtained and the universal formula obtained from many (2+1)-dimensional systems is extended or modified.
