The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions ...The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions between two breathers,a breather/lump and line solitons as well as lump molecules for the(2+1)-dimensional elliptic Toda equation.Based on the N-soliton solution,we obtain the hybrid solutions consisting of line solitons,breathers and lumps.Through the asymptotic analysis of these hybrid solutions,we derive the phase shifts of the breather,lump and line solitons before and after the interaction between a breather/lump and line solitons.By making the phase shifts infinite,we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons.Through the asymptotic analysis of these resonant solutions,we demonstrate that the resonant interactions exhibit the fusion,fission,time-localized breather and rogue lump phenomena.Utilizing the velocity resonance method,we obtain lump–soliton,lump–breather,lump–soliton–breather and lump–breather–breather molecules.The above works have not been reported in the(2+1)-dimensional discrete nonlinear wave equations.展开更多
This research studied the flow boiling heat transfer characteristics in vertical rectangular channel with 2mm gap width under the thermosiphon circulation.It was found that convective evaporation heat transfer somehti...This research studied the flow boiling heat transfer characteristics in vertical rectangular channel with 2mm gap width under the thermosiphon circulation.It was found that convective evaporation heat transfer somehtimes was in a transitional flow state,the calculation method was not reported.An equation for convective evaporation was developed and was suitable for the calculations of laminar,transition and turbulent flow states.The absolute deviation of the calculated flow boiling heat transfer coefficient from the experimental data was 14.9% by this method.展开更多
In this paper, we investigate a modified differential-difference KP equation which is shown to have a continuum limit into the m KP equation. It is also shown that the solution of the modified differential-difference ...In this paper, we investigate a modified differential-difference KP equation which is shown to have a continuum limit into the m KP equation. It is also shown that the solution of the modified differential-difference KP equation is related to the solution of the differential-difference KP equation through a Miura transformation. We first present the Grammian solution to the modified differential-difference KP equation, and then produce a coupled modified differential-difference KP system by applying the source generation procedure. The explicit N-soliton solution of the resulting coupled modified differential-difference system is expressed in compact forms by using the Grammian determinant and Casorati determinant. We also construct and solve another form of the self-consistent sources extension of the modified differential-difference KP equation, which constitutes a B?cklund transformation for the differentialdifference KP equation with self-consistent sources.展开更多
基金the National Natural Science Foundation of China(Grant Nos.12061051 and 11965014)。
文摘The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions between two breathers,a breather/lump and line solitons as well as lump molecules for the(2+1)-dimensional elliptic Toda equation.Based on the N-soliton solution,we obtain the hybrid solutions consisting of line solitons,breathers and lumps.Through the asymptotic analysis of these hybrid solutions,we derive the phase shifts of the breather,lump and line solitons before and after the interaction between a breather/lump and line solitons.By making the phase shifts infinite,we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons.Through the asymptotic analysis of these resonant solutions,we demonstrate that the resonant interactions exhibit the fusion,fission,time-localized breather and rogue lump phenomena.Utilizing the velocity resonance method,we obtain lump–soliton,lump–breather,lump–soliton–breather and lump–breather–breather molecules.The above works have not been reported in the(2+1)-dimensional discrete nonlinear wave equations.
文摘This research studied the flow boiling heat transfer characteristics in vertical rectangular channel with 2mm gap width under the thermosiphon circulation.It was found that convective evaporation heat transfer somehtimes was in a transitional flow state,the calculation method was not reported.An equation for convective evaporation was developed and was suitable for the calculations of laminar,transition and turbulent flow states.The absolute deviation of the calculated flow boiling heat transfer coefficient from the experimental data was 14.9% by this method.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11601247 and 11605096the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant Nos.2016MS0115 and 2015MS0116the Innovation Fund Programme of Inner Mongolia University No.201611155
文摘In this paper, we investigate a modified differential-difference KP equation which is shown to have a continuum limit into the m KP equation. It is also shown that the solution of the modified differential-difference KP equation is related to the solution of the differential-difference KP equation through a Miura transformation. We first present the Grammian solution to the modified differential-difference KP equation, and then produce a coupled modified differential-difference KP system by applying the source generation procedure. The explicit N-soliton solution of the resulting coupled modified differential-difference system is expressed in compact forms by using the Grammian determinant and Casorati determinant. We also construct and solve another form of the self-consistent sources extension of the modified differential-difference KP equation, which constitutes a B?cklund transformation for the differentialdifference KP equation with self-consistent sources.
