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1.
利用hirota双线性法,得到(3+1)维孤子方程、(3+1)维KP-Boussinesq方程、(2+1)维修正Caudrey-Dodd-Gibbon-Kotera-S awada方程、Hirota-Satsuma浅水波方程的精确解,并做出一部分解的图形,进一步研究解的结构和性质.  相似文献   
2.
We address the problem of telegraphic transport in several dimensions. We review the derivation of two and three dimensional telegrapher’s equations—as well as their fractional generalizations—from microscopic random walk models for transport (normal and anomalous). We also present new results on solutions of the higher dimensional fractional equations.  相似文献   
3.
A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.  相似文献   
4.
利用孤立子方程KdV-mKdV的朗斯基解的形式和结构,我们提出了朗斯基形式展开法,运用这一方法获得了KdV-mKdV方程的丰富的新的复合函数解,并且朗斯基行列式中的元素不满足任何线性偏微分方程组.所得到的复合函数解是使用其它的方法得不到的.  相似文献   
5.
近年来以低温室效应(GWP)的制冷剂的蒸汽压缩式高温热泵一直是余热回收领域的研究热点。为获得更高的输出温度,本课题组搭建了一台采用自然工质水作为循环冷媒的超高温热泵样机并进行了实验测试。实验结果表明蒸发温度为80℃,冷凝温度从115℃升至145℃时,热泵的COP从4.88降至1.89。在85℃蒸发,117℃冷凝时,最高COP为6.1,制热量为285 kW,同时在85℃蒸发时,该热泵的最高冷凝温度可达到150℃,此时COP为1.96。在相同的温升下,热泵的COP和卡诺效率都随着输出温度的升高而增加,因此我们认为该热泵更适合高温输出的应用场合。  相似文献   
6.
李军  陈勇 《理论物理通讯》2021,73(1):15001-5
Despite some empirical successes for solving nonlinear evolution equations using deep learning,there are several unresolved issues.First,it could not uncover the dynamical behaviors of some equations where highly nonlinear source terms are included very well.Second,the gradient exploding and vanishing problems often occur for the traditional feedforward neural networks.In this paper,we propose a new architecture that combines the deep residual neural network with some underlying physical laws.Using the sine-Gordon equation as an example,we show that the numerical result is in good agreement with the exact soliton solution.In addition,a lot of numerical experiments show that the model is robust under small perturbations to a certain extent.  相似文献   
7.
Ying Yang 《中国物理 B》2021,30(11):110202-110202
The research of rogue waves is an advanced field which has important practical and theoretical significances in mathematics, physics, biological fluid mechanics, oceanography, etc. Using the reductive perturbation theory and long wave approximation, the equations governing the movement of blood vessel walls and the flow of blood are transformed into high-order nonlinear Schrödinger (NLS) equations with variable coefficients. The third-order nonlinear Schrödinger equation is degenerated into a completely integrable Sasa-Satsuma equation (SSE) whose solutions can be used to approximately simulate the real rogue waves in the vessels. For the first time, we discuss the conditions for generating rogue waves in the blood vessels and effects of some physiological parameters on the rogue waves. Based on the traveling wave solutions of the fourth-order nonlinear Schrödinger equation, we analyze the effects of the higher order terms and the initial deformations of the blood vessel on the wave propagation and the displacement of the tube wall. Our results reveal that the amplitude of the rogue waves are proportional to the initial stretching ratio of the tube. The high-order nonlinear and dispersion terms lead to the distortion of the wave, while the initial deformation of the tube wall will influence the wave amplitude and wave steepness.  相似文献   
8.
使用Galerkin方法,结合Sobolev空间理论和不等式技巧,给出了广义神经传播方程解的存在唯一性定理,然后利用吸引子存在性定理,采用半群方法证明了方程整体吸引子的存在性.  相似文献   
9.
本文采用SST湍流模型模拟了类前缘通道内蒸汽射流阵列冲击冷却的流动与传热特性,分析了雷诺数(Re=10000~50000)、孔径比(d/H=0.5~0.9)和孔间距比(S/H=2~6)对流动及传热性能的影响规律,得到了相应的传热和摩擦关联式。结果表明:在不同雷诺数下,d/H从0.5到0.9变化时,通道压力损失系数降低了76%~79%,靶面平均努塞尔数降低了45%~49%;S/H从2增至6时,通道压力损失系数增加了1.64~1.92倍,靶面平均努塞尔数增加了54%~64%;增大d/H、减小S/H可有效提高类前缘通道蒸汽冲击冷却的综合热力系数。本文研究结果可为未来先进燃气轮机高温涡轮叶片蒸汽冷却结构的设计提供参考和借鉴。  相似文献   
10.
We have performed numerical analysis of the one-dimensional dynamics of the cylindrical/spherical dust ion acoustic shock waves in unmagnetized dusty plasma consisting of positive ions, immobile dust particles, and nonextensive distributed cold and hot electrons. A multiple-scale expansion method is used to derive Burgers Equation (BE) and modified Burgers equation (MBE) by including higher order nonlinearity. The basic characteristics of the shock waves have been analysed numerically and graphically for different physical parameters relevant to Saturn' E ring through 2D figures. The parametric dependence of dust ion acoustic shock waves on some plasma parameters nonextensive index, density, and temperature of cold and hot electrons, concentration of dust particles, thermal effects and kinematic viscosity of ions is explored. Furthermore, it is found that the nonplanar geometry effects have an important impact on the establishment of shock waves. The amplitude of the wave decreases faster as one departs away from the axis of the cylinder or centre of the sphere. Such decaying behaviour continues as time progresses. It is also found that an increasing dust concentration decreases the amplitude of the dust ion acoustic shock waves.  相似文献   
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