检索结果-南通市图书馆

A maple package for the Painleve Test of nonlinear partial differential equations

在线全文

学校读者我要写书评

暂无评论

Chinese Physics Letters 2003年第7期20卷 975-978页

作者：徐桂琼李志斌 DepartmentofComputerScience EastChinaNormalUniversityShanghai200062 DepartmentofInformationAdministration ShanghaiUniversityShanghai200436 DepartmentofComputerScience EastChinaNormalUniversityShanghai200062

A Maple package, named PLtest, is presented to study whether or not nonlinear partial differential equations (PDEs) pass the Painlevé test. This package is based on the so-called WTC-Kruskal algorithm, which combines the standard WTC algorithm and the Kruskal simplification algorithm. Therefore, we not only study whether the given PDEs pass the test or not, but also obtain its truncated expansion form related to some integrability properties. Several well-known nonlinear models with physical interests illustrate the effectiveness of this package.

关键词： Maple Package Painleve Test nonlinear partial differential equations

Weak Continuity and Compactness for nonlinear partial differential equations

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2015年第5期36卷 715-736页

作者： Gui-Qiang G.CHEN School of Mathematical Sciences Fudan University Academy of Mathematics and Systems Science Chinese Academy of Sciences Mathematical Institute University of Oxford

This paper presents several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. The compactness and convergence of vanishing viscosity solutions for nonlinear hyperbolic conservation laws are first analyzed, including the inviscid limit from the Navier-Stokes equations to the Euler equations for homentropic flow, the vanishing viscosity method to construct the global spherically symmetric solutions to the multidimensional compressible Euler equations, and the sonic-subsonic limit of solutions of the full Euler equations for multi-dimensional steady compressible fluids. Then the weak continuity and rigidity of the Gauss-Codazzi-Ricci system and corresponding isometric embeddings in differential geometry are revealed. Further references are also provided for some recent developments on the weak continuity and compactness for nonlinear partial differential equations.

关键词： Weak continuity Compensated compactness nonlinear partial differential equations Euler equations Gauss-Codazzi-Ricci system

Sparse Deep Neural Network for nonlinear partial differential equations

在线全文

学校读者我要写书评

暂无评论

Numerical Mathematics(Theory,Methods and Applications) 2023年第1期16卷 58-78页

作者： Yuesheng Xu Taishan Zeng Department of Mathematics and Statistics Old Dominion UniversityNorfolkVirginia 23529USA School of Mathematical Science South China Normal UniversityGuangzhou 510631China Guangdong Key Laboratory of Big Data Analysis and Processing Guangzhou 510006China

More competent learning models are demanded for data processing due to increasingly greater amounts of data available in *** that we encounter often have certain embedded sparsity *** is,if they are represented in an appropriate basis,their energies can concentrate on a small number of basis *** paper is devoted to a numerical study of adaptive approximation of solutions of nonlinear partial differential equations whose solutions may have singularities,by deep neural networks(DNNs)with a sparse regularization with multiple *** that DNNs have an intrinsic multi-scale structure which is favorable for adaptive representation of functions,by employing a penalty with multiple parameters,we develop DNNs with a multi-scale sparse regularization(SDNN)for effectively representing functions having certain *** then apply the proposed SDNN to numerical solutions of the Burgers equation and the Schrödinger *** examples confirm that solutions generated by the proposed SDNN are sparse and accurate.

关键词： Sparse approximation deep learning nonlinear partial differential equations sparse regularization adaptive approximation

Modified Laguerre spectral and pseudospectral methods for nonlinear partial differential equations in multiple dimensions

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Applied Mathematics and Mechanics(English Edition) 2008年第3期29卷 311-331页

作者：徐承龙郭本瑜 Department of Mathematics Tongji University Division of Computational Science of E-institute of Shanghai Universities

The Laguerre spectral and pseudospectral methods are investigated for multidimensional nonlinear partial differential equations. Some results on the modified Laguerre orthogonal approximation and interpolation are established, which play important roles in the related numerical methods for unbounded domains. As an example, the modified Laguerre spectral and pseudospectral methods are proposed for two-dimensional Logistic equation. The stability and convergence of the suggested schemes are proved. Numerical results demonstrate the high accuracy of these approaches.

关键词： modified Laguerre orthogonal approximation and interpolation multiple dimensions spectral and pseudospectral methods nonlinear partial differential equations

Extended Mapping Transformation Method and Its Applications to nonlinear partial differential Equation（s）

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2005年第3X期44卷 473-478页

作者： ZHAO Hong BAI Cheng-Lin Physics Science and Information Engineering School Liaocheng University Liaocheng 252059 China

In this paper, we extend the mapping transformation method through introducing variable *** means of the extended mapping transformation method, many explicit and exact general solutions with arbitrary functions for some nonlinear partial differential equations, which contain solitary wave solutions, trigonometric function solutions, and rational solutions, are obtained.

关键词： nonlinear partial differential equations extended mapping transformation method exact solutions

Solutions to mKdV Eequation of Electromagnetic Wave Propagation in Cold Collisionless Plasma

在线全文

学校读者我要写书评

暂无评论

Plasma Science and Technology 2006年第5期8卷 505-510页

作者：翁建平 Department of Physics Lishui College Lishui 323000 China

The equation of electromagnetic wave propagation through cold collisionless plasma can be reduced to the modified Kortweg-de Vries （mKdV） equation. Using a new technique, whose keys are the trial solution in terms of the exponential function and the ideas of the like-terms＇ balance, some groups of accurate analytical solutions for this mKdV equation, such as solitary wave solutions, can be obtained. It is successfully shown that this method may be still valid for solving other nonlinear plasma equations.

关键词： nonlinear partial differential equations mKdV equation collisionless plasma

A new variable coefficient algebraic method and non-travelling wave solutions of nonlinear equations

在线全文

学校读者我要写书评

暂无评论

Chinese Physics B 2008年第11期17卷 3974-3984页

作者：陆斌张鸿庆 Department of Applied Mathematics Dalian University of Technology

In this paper, a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the validity and the advantages of the method, （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation is employed and many new double periodic non-travelling wave solutions are obtained. This algorithm can also be applied to other nonlinear differential equations.

关键词： nonlinear partial differential equations non-travelling wave solutions asymmetric Nizhnik-Novikov- Vesselov equation

EXISTENCE, BOUNDEDNESS AND UNIQUENESS OF WEAK SOLUTION FOR THE THERMISTOR PROBLEM WITH MIXED BOUNDARV CONDITIONS

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 1998年第3期18卷 326-332页

作者：管平 Southeast University Nanjing 210096 China

The thermistor problem is a coupled system of nonlinear PDEs with mixed boundary conditions. The goal of this paper is to study the existence, boundedness and uniqueness of the weak solution for this problem.

关键词： nonlinear partial differential equations existence,boundedness uniqueness

Travelling wave solutions of nonlinear conformable analytical approaches

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics(A Journal of Chinese Universities) 2024年第3期39卷 502-518页

作者： Hira Tariq Hira Ashraf Hadi Rezazadeh Ulviye Demirbilek Department of Mathematics Government College Women UniversitySialkotPakistan Faculty of Engineering Technology Amol University of Special Modern TechnologiesAmolIran Faculty of Arts and Sciences Department of MathematicsMersin UniversityMersinTurkey

The presented study deals with the investigation of nonlinear Bogoyavlenskii equations with conformable time-derivative which has great importance in plasma physics and non-inspectoral scattering *** wave solutions of this nonlinear conformable model are constructed by utilizing two powerful analytical approaches,namely,the modified auxiliary equation method and the Sardar sub-equation *** novel soliton solutions are extracted using these ***,3D surface graphs,contour plots and parametric graphs are drawn to show dynamical behavior of some obtained solutions with the aid of symbolic software such as *** constructed solutions will help to understand the dynamical framework of nonlinear Bogoyavlenskii equations in the related physical phenomena.

关键词： nonlinear partial differential equations modified auxiliary equation method Sardar sub-equation method soliton solutions