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Numerical Methods for a Class of Quadratic Matrix Equations
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作者 GUAN Jinrui WANG Zhixin SHAO Rongxia 《应用数学》 北大核心 2024年第4期962-970,共9页
Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of... Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper. 展开更多
关键词 Quadratic matrix equation M-MATRIX Minimal nonnegative solution Newton method bernoulli method
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Confirmation of the First Law of Thermodynamics in Theory and Extended Bernoulli Equation
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作者 Chengshu Jin 《Journal of Applied Mathematics and Physics》 2023年第2期409-420,共12页
The internal energy change of ideal gas does not depend on the volume and pressure. The internal energy change of real gas has not any relation with the volume and pressure, which had been proved. If the internal ener... The internal energy change of ideal gas does not depend on the volume and pressure. The internal energy change of real gas has not any relation with the volume and pressure, which had been proved. If the internal energy change had not any relation with the volume and pressure, we could confirm the first law of thermodynamics in theory. Simultaneously, the internal energy change is the state function that shall be able to be proved in theory. If the internal energy change depended on the volume and pressure, we could not prove that the internal energy change is the state function and the chemical thermodynamics theory is right. The extended or modified Bernoulli equation can be derived from the energy conservation law, and the internal energy change, heat, and friction are all considered in the derivation procedure. The extended Bernoulli equation could be applied to the flying aircraft and mechanical motion on the gravitational field, for instance, the rocket and airplane and so on. This paper also revises some wrong ideas, viewpoints, or concepts about the thermodynamics theory and Bernoulli equation. 展开更多
关键词 First Law of Thermodynamics Chemical Thermodynamics bernoulli equation Static Pressure Head FRICTION
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THRESHOLD RESULT FOR SEMILINEAR PARABOLIC EQUATIONS WITH INDEFINITE NON-HOMOGENEOUS TERM
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作者 谢君辉 戴求亿 刘芳 《Acta Mathematica Scientia》 SCIE CSCD 2012年第6期2302-2314,共13页
In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations {μt-△μ=g(μ)+λf(x),(x,t)∈Ω×(0,T),μ=0,(x,t)∈ Ω×[0,T)... In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations {μt-△μ=g(μ)+λf(x),(x,t)∈Ω×(0,T),μ=0,(x,t)∈ Ω×[0,T),μ(x,0)=μ0(x)≥0,x∈Ω.By combining a priori estimate of global solution with property of stationary solution set of problem (P), we prove that the minimal stationary solution Uλ(x) of problem (P) is stable, whereas, any other stationary solution is an initial datum threshold for the existence and nonexistence of global solution to problem (P). 展开更多
关键词 parabolic equations initial boundary value problem global solution thresh-old result non-homogenous tern:
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An Elliptic Gradient Estimate for A Non-homogeneous Heat Equation on Complete Noncompact Manifolds
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作者 JI Xiang 《Chinese Quarterly Journal of Mathematics》 2018年第1期61-67,共7页
Let M be an n-dimensional complete noncompact Riemannian manifold. In this paper, we will give the elliptic gradient estimate for positive smooth solutions to the non-homogeneous heat equation(?_t-△)u(x, t) = A(x, t)... Let M be an n-dimensional complete noncompact Riemannian manifold. In this paper, we will give the elliptic gradient estimate for positive smooth solutions to the non-homogeneous heat equation(?_t-△)u(x, t) = A(x, t)when the metric evolves under the Ricci flow. As applications, we get Harnack inequalities to compare solutions at the same time. 展开更多
关键词 non-homogeneous heat equation Ricci flow Bochner formula elliptic type gradient estimate Harnack inequality
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含多维随机变量的广义概率密度演化方程解析解:以Euler-Bernoulli梁为例
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作者 周永峰 李杰 《力学学报》 EI CAS CSCD 北大核心 2024年第9期2659-2668,共10页
广义概率密度演化方程的解析解,不仅具有重要理论价值,而且具有校验数值解、进而标定数值算法误差的作用.以Euler-Bernoulli简支梁为例,推导给出了梁受迫振动时跨中位移响应所对应的广义概率密度演化方程解析解.包括非平稳非高斯随机载... 广义概率密度演化方程的解析解,不仅具有重要理论价值,而且具有校验数值解、进而标定数值算法误差的作用.以Euler-Bernoulli简支梁为例,推导给出了梁受迫振动时跨中位移响应所对应的广义概率密度演化方程解析解.包括非平稳非高斯随机载荷作用下的解(包含2维随机变量)以及同时考虑载荷随机性和结构参数随机性时的解(分别包含2维、4维和5维随机变量).分析结果表明,真实的概率密度演化是一个十分复杂的过程,远不能用简单的概率分布函数加以描述.这一进展,可为概率密度演化理论的进一步深入研究提供一个方面的基础. 展开更多
关键词 广义概率密度演化方程 解析解 Euler-bernoulli 受迫振动 多维随机变量
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Bernoulli’s Equation with Acceleration
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作者 Kern E. Kenyon 《Natural Science》 2015年第10期488-490,共3页
For steady frictionless flow along a straight line, when a constant acceleration is applied parallel to that line, a term needs to be added to the standard form of Bernoulli’s equation. After so modifying, the equati... For steady frictionless flow along a straight line, when a constant acceleration is applied parallel to that line, a term needs to be added to the standard form of Bernoulli’s equation. After so modifying, the equation then predicts that along a streamline, when the speed is high, the pressure is significantly lower than that if there were no acceleration. For example, one might think of a dense fluid falling down through a less dense fluid under gravity. Potential applications to vertical motions of the atmosphere, such as down bursts of cold dry air and warm humid updrafts in the eye of a hurricane, are mentioned. 展开更多
关键词 bernoulli’s equation ACCELERATED MOTION
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Euler-Bernoulli方程在混合边界控制下的能量指数衰减
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作者 白忠玉 《西北师范大学学报(自然科学版)》 CAS 2024年第5期104-109,共6页
研究一类Euler-Bernoulli方程的能量衰减问题.在混合边界控制下,利用耗散反馈算子和变量替换,建立了能量衰减不等式,证明了Euler-Bernoulli方程解的能量是指数衰减的.
关键词 Euler-bernoulli方程 混合边界控制 指数衰减 反馈算子 变量替换
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Numerical Solution of Euler-Bernoulli Beam Equation by Using Barycentric Lagrange Interpolation Collocation Method
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作者 Haolu Zhang Lianwang Chen Lei Fu 《Journal of Applied Mathematics and Physics》 2021年第4期594-605,共12页
Euler-Bernoulli beam equation is very important that can be applied in the field of mechanics, science and technology. Some authors have put forward many different numerical methods, but the precision is not enough hi... Euler-Bernoulli beam equation is very important that can be applied in the field of mechanics, science and technology. Some authors have put forward many different numerical methods, but the precision is not enough high. In this paper, we will illustrate the high-precision numerical method to solve Euler-Bernoulli beam equation. Three numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by our method indicate new algorithm has the following advantages: small computational work, fast convergence speed and high precision. 展开更多
关键词 Barycentric Interpolation Collocation Method Euler-bernoulli Beam equation Linearized Iterative
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Global Existence and Large Time Asymptotic Behavior of Strong Solution to the Cauchy Problem of 2D Density-Dependent Boussinesq Equations with Vacuum 被引量:1
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作者 Min Liu 《Journal of Applied Mathematics and Physics》 2019年第10期2333-2351,共19页
We dedicate to the 2D density-dependent nonhomogeneous incompressible Boussinesq equations with vacuum on . At infinity, if the attenuation of initial density and temperature is not very slow. And it is gained that th... We dedicate to the 2D density-dependent nonhomogeneous incompressible Boussinesq equations with vacuum on . At infinity, if the attenuation of initial density and temperature is not very slow. And it is gained that there is a global strong solution and is unique for the 2D Cauchy problem with the initial density which can allow vacuum conditions and even have compact support. Besides, the large time decay rates of the gradients of velocity, temperature and pressure can also be obtained which are also the same as those of the homogeneous case. 展开更多
关键词 non-homogeneous Incompressible BOUSSINESQ equation Strong Solution LARGE TIME Behavior Existence and Uniqueness
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THE EXTINCTION BEHAVIOR OF THE SOLUTIONS FOR A CLASS OF REACTION-DIFFUSION EQUATIONS
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作者 CHEN Song-lin(陈松林) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第11期1352-1356,共5页
The methods of L-p estimation are used to discuss the extinction phenomena of the solutions to the following reaction-diffusion equations with initial-boundary values partial derivativeu/partial derivativet = Deltau -... The methods of L-p estimation are used to discuss the extinction phenomena of the solutions to the following reaction-diffusion equations with initial-boundary values partial derivativeu/partial derivativet = Deltau - lambda \u\(gamma-1) u - betau ((x, t) is an element of Omega x (0, + infinity)), u(x, t) \(partial derivativeOmegax (0, +infinity)) = 0, u(x, 0) = u(0) (x) is an element of H-0(1) (Omega) boolean AND L1+gamma(Omega) (x is an element of Omega). Sufficient and necessary conditions about the extinction of the solutions is given. Here lambda > 0, gamma > 0, beta > 0 are constants, Omega is an element of R-N is bounded with smooth boundary partial derivativeOmega. At last, it is simulated with a higher order equation by using the present methods. 展开更多
关键词 reaction-diffusion equation EXTINCTION L-p estimation bernoulli equation
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Contribution to the Analytical Equation Resolution Using Charts for Analysis and Design of Cylindrical and Conical Open Surge Tanks
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作者 Aboudou Seck Musandji Fuamba 《Journal of Water Resource and Protection》 2015年第15期1242-1256,共15页
In the event of an instantaneous valve closure, the pressure transmitted to a surge tank induces the mass fluctuations that can cause high amplitude of water-level fluctuation in the surge tank for a reasonable cross-... In the event of an instantaneous valve closure, the pressure transmitted to a surge tank induces the mass fluctuations that can cause high amplitude of water-level fluctuation in the surge tank for a reasonable cross-sectional area. The height of the surge tank is then designed using this high water level mark generated by the completely closed penstock valve. Using a conical surge tank with a non-constant cross-sectional area can resolve the problems of space and height. When addressing issues in designing open surge tanks, key parameters are usually calculated by using complex equations, which may become cumbersome when multiple iterations are required. A more effective alternative in obtaining these values is the use of simple charts. Firstly, this paper presents and describes the equations used to design open conical surge tanks. Secondly, it introduces user-friendly charts that can be used in the design of cylindrical and conical open surge tanks. The contribution can be a benefit for practicing engineers in this field. A case study is also presented to illustrate the use of these design charts. The case study’s results show that key parameters obtained via successive approximation method required 26 iterations or complex calculations, whereas these values can be obtained by simple reading of the proposed chart. The use of charts to help surge tanks designing, in the case of preliminary designs, can save time and increase design efficiency, while reducing calculation errors. 展开更多
关键词 Hydraulic Transients SURGE Tank Water HAMMER FIRST-ORDER non-homogeneous Differential equation with Variables COEFFICIENTS Friendly Charts
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A Computational Quadruple Laplace Transform for the Solution of Partial Differential Equations
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作者 Hamood Ur Rehman Muzammal Iftikhar +2 位作者 Shoaib Saleem Muhammad Younis Abdul Mueed 《Applied Mathematics》 2014年第21期3372-3382,共11页
In this paper, we proposed new results in quadruple Laplace transform and proved some properties concerned with quadruple Laplace transform. We also developed some applications based on these results and solved homoge... In this paper, we proposed new results in quadruple Laplace transform and proved some properties concerned with quadruple Laplace transform. We also developed some applications based on these results and solved homogeneous as well as non-homogeneous partial differential equations involving four variables. The performance of quadruple Laplace transform is shown to be very encouraging by concrete examples. An elementary table of quadruple Laplace transform is also provided. 展开更多
关键词 Quadruple LAPLACE Transform EXACT SOLUTION CONVOLUTION Partial Differential equation Homogeneous and non-homogeneous Problems
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Local Strong Solutions for the Cauchy Problem of 2D Density-Dependent Boussinesq Equations with Vacuum
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作者 Huifeng Wang 《Journal of Applied Mathematics and Physics》 2019年第10期2373-2383,共11页
The main goal of the paper is to obtain the local strong solution of the Cauchy problem of the nonhomogeneous incompressible Boussinesq equation in two-dimension space. Especially, when the far-field density is vacuum... The main goal of the paper is to obtain the local strong solution of the Cauchy problem of the nonhomogeneous incompressible Boussinesq equation in two-dimension space. Especially, when the far-field density is vacuum, we make a priori estimate in a bound ball and prove the existence and uniqueness of the local strong solution of the Boussinesq equation. 展开更多
关键词 non-homogeneous INCOMPRESSIBLE BOUSSINESQ equation Strong Solution VACUUM CAUCHY Problem
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A Split-Step Predictor-Corrector Method for Space-Fractional Reaction-Diffusion Equations with Nonhomogeneous Boundary Conditions
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作者 Kamran Kazmi Abdul Khaliq 《Communications on Applied Mathematics and Computation》 2019年第4期525-544,共20页
A split-step second-order predictor-corrector method for space-fractional reaction-diffusion equations with nonhomogeneous boundary conditions is presented and analyzed for the stability and convergence.The matrix tra... A split-step second-order predictor-corrector method for space-fractional reaction-diffusion equations with nonhomogeneous boundary conditions is presented and analyzed for the stability and convergence.The matrix transfer technique is used for spatial discretization of the problem.The method is shown to be unconditionally stable and second-order convergent.Numerical experiments are performed to confirm the stability and secondorder convergence of the method.The split-step predictor-corrector method is also compared with an IMEX predictor-corrector method which is found to incur oscillatory behavior for some time steps.Our method is seen to produce reliable and oscillatioresults for any time step when implemented on numerical examples with nonsmooth initial data.We also present a priori reliability constraint for the IMEX predictor-corrector method to avoid unwanted oscillations and show its validity numerically. 展开更多
关键词 FRACTIONAL LAPLACIAN Space-fractional reaction diffusion equations non-homogeneous boundary conditions Matrix transfer technique PREDICTOR-CORRECTOR method
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Local Regularity for a 1D Compressible Viscous Micropolar Fluid Model with Non-homogeneous Temperature Boundary
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作者 SUN Lin-lin LIANG Tie-wang ZHANG Jian-peng 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第1期129-141,共13页
In this paper,we discuss the local existence of H^i(i=2,4)solutions for a 1D compressible viscous micropolar fluid model with non-homogeneous temperature boundary.The proof is based on the local existence of solutions... In this paper,we discuss the local existence of H^i(i=2,4)solutions for a 1D compressible viscous micropolar fluid model with non-homogeneous temperature boundary.The proof is based on the local existence of solutions in[1]. 展开更多
关键词 compressible Navier-Stokes equations micropolar fluid the initial boundary value problem non-homogeneous temperature boundary
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Global Solutions and Interactions of Non-selfsimilar Elementary Waves for n-D Non-homogeneous Burgers Equation
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作者 Yuan-an ZHAO Gao-wei CAO Xiao-zhou YANG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2023年第4期830-853,共24页
We investigate the global structures of the non-selfsimilar solutions for n-dimensional(n-D) nonhomogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a(n-1)-... We investigate the global structures of the non-selfsimilar solutions for n-dimensional(n-D) nonhomogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a(n-1)-dimensional sphere. We first obtain the expressions of n-D shock waves and rarefaction waves emitting from the initial discontinuity. Then, by estimating the new kind of interactions of the related elementary waves,we obtain the global structures of the non-selfsimilar solutions, in which ingenious techniques are proposed to construct the n-D shock waves. The asymptotic behaviors with geometric structures are also proved. 展开更多
关键词 non-homogeneous burgers equation n-dimensional Riemann problem global singular structure non-selfsimilar solution interactions of elementary waves
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关于欧拉方程和伯努利方程适用条件的探讨
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作者 张仪萍 邵煜 +2 位作者 张土乔 张燕 周永潮 《力学与实践》 2024年第5期1059-1065,共7页
从动量守恒和能量守恒出发,详细地阐述了欧拉方程和伯努利方程的推导过程。从两个方程的推导过程可以清楚地看到,欧拉方程适用的充要条件是黏性偏应力张量的散度为零,流体黏度为零只是欧拉方程成立的充分条件而非必要条件。伯努利方程... 从动量守恒和能量守恒出发,详细地阐述了欧拉方程和伯努利方程的推导过程。从两个方程的推导过程可以清楚地看到,欧拉方程适用的充要条件是黏性偏应力张量的散度为零,流体黏度为零只是欧拉方程成立的充分条件而非必要条件。伯努利方程除了需要适用欧拉方程外,还需要满足流体正压、质量力有势、流动定常的条件,如果需要保持系统的总能量守恒,则正压流体条件需改为等熵流动条件。 展开更多
关键词 欧拉方程 伯努利方程 理想流体 等熵流动 绝热流动
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工程流体力学叙事型课堂设计及实施研究
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作者 林培锋 王蕊 胡箫 《力学与实践》 2024年第3期663-668,共6页
鉴于新工科对高等教育的要求,结合注意力经济时代学生难以被课堂吸引的现状,提出了基于三幕式叙事模式的课堂设计思路,从时长分配、内容安排和注意力抓取3个方面,探究了工程流体力学课程的宏观课程编排和具体课堂设计改进思路,并以伯努... 鉴于新工科对高等教育的要求,结合注意力经济时代学生难以被课堂吸引的现状,提出了基于三幕式叙事模式的课堂设计思路,从时长分配、内容安排和注意力抓取3个方面,探究了工程流体力学课程的宏观课程编排和具体课堂设计改进思路,并以伯努利方程章节为例,给出了叙事型课堂具体的实施流程,激发学生课上课下自主学习的兴趣,提高学生的创新动力和解决实际工程问题的能力。 展开更多
关键词 叙事型课堂 课堂设计 工程流体力学 伯努利方程
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在小间隙放电中用Bernoulli定理分析电极移动速度效应 被引量:10
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作者 阮方鸣 石丹 +3 位作者 高攸纲 杨乘 周锋 刘素玲 《电波科学学报》 EI CSCD 北大核心 2009年第3期551-555,共5页
小间隙静电放电中电极移动速度对放电参数影响的内部因素,是受到很多研究者关心的问题。通过对实验数据的系统分析,应用流体力学中Bernoulli定律,对放电参数电极速度效应的内部原因,提出了较好的理论解释。电极的快速运动速度造成了放... 小间隙静电放电中电极移动速度对放电参数影响的内部因素,是受到很多研究者关心的问题。通过对实验数据的系统分析,应用流体力学中Bernoulli定律,对放电参数电极速度效应的内部原因,提出了较好的理论解释。电极的快速运动速度造成了放电间隙气体压强的下降,从而加速了载流子从电极到靶的运动过程,进而明显改变了放电参数的数值。初步的数值计算表明,表面过程因电极快速移动得到了加强。这对于电极移动速度效应进一步的研究,给出了一种较为明确的方向。 展开更多
关键词 速度效应 bernoulli方程 静电放电 气体压强
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基于Riccati-Bernoulli辅助常微分方程的Davey-Stewartson方程的行波解 被引量:9
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作者 杨小锋 邓子辰 魏乙 《应用数学和力学》 CSCD 北大核心 2015年第10期1067-1075,共9页
Riccati-Bernoulli辅助常微分方程方法可以用来构造非线性偏微分方程的行波解.利用行波变换,将非线性偏微分方程化为非线性常微分方程,再利用Riccati-Bernoulli方程将非线性常微分方程化为非线性代数方程组,求解非线性代数方程组就能直... Riccati-Bernoulli辅助常微分方程方法可以用来构造非线性偏微分方程的行波解.利用行波变换,将非线性偏微分方程化为非线性常微分方程,再利用Riccati-Bernoulli方程将非线性常微分方程化为非线性代数方程组,求解非线性代数方程组就能直接得到非线性偏微分方程的行波解.对Davey-Stewartson方程应用这种方法,得到了该方程的精确行波解.同时也得到了该方程的一个Bcklund变换.所得结果与首次积分法的结果作了比较.Riccati-Bernoulli辅助常微分方程方法是一种简单、有效地求解非线性偏微分方程精确解的方法. 展开更多
关键词 Riccati—bernoulli辅助常微分方程方法 Davey—Stewartson方程 行波解 BACKLUND变换
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