检索结果-南通市图书馆

Nonuniform Dependence on the Initial Data for Solutions of conservation laws

在线全文

学校读者我要写书评

暂无评论

Communications on Applied Mathematics and Computation 2024年第1期6卷 489-500页

作者： John M.Holmes Barbara Lee Keyfitz Department of Mathematics The Ohio State UniversityColumbusOH43210USA

In this paper,we study systems of conservation laws in one space dimension.We prove that for classical solutions in Sobolev spaces H^(s),with s>3/2,the data-to-solution map is not uniformly continuous.Our results appl... 详细信息

关键词： conservation laws Data-to-solution map Nonuniform dependence

Construction of conservation laws for the Gardner equation,Landau-Ginzburg-Higgs equation,and Hirota-Satsuma equation

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2024年第5期76卷 49-57页

作者： Cheng Chen Faiza Afzal Yufeng Zhang School of Mathematics China University of Mining and TechnologyXuzhou221116China Jiangsu Center for Applied Mathematics(CUMT) XuzhouJiangsu 221116China

In this paper,two different methods for calculating the conservation laws are used,these are the direct construction of conservation laws and the conservation theorem proposed by Ibragimov.Using these two methods,we obtain the conservation laws of the Gardner equation,Landau-Ginzburg-Higgs equation and Hirota-Satsuma equation,respectively.

关键词： conservation laws Landau-Ginzburg-Higgs equation Hirota-Satsuma equation Gardner equation

conservation laws of the complex short pulse equation and coupled complex short pulse equations

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2022年第7期74卷 49-56页

作者： Lihua Zhang Bo Shen Shuxin Han Gangwei Wang Lingshu Wang School of Mathematics and Statistics Hebei University of Economics and BusinessShijiazhuang 050061China

In this paper, the complex short pulse equation and the coupled complex short pulse equations that can describe the ultra-short pulse propagation in optical fibers are investigated. The two complex nonlinear models are turned into multi-component real models by proper transformations. Lie symmetries are obtained via the classical Lie group method, and the results for the coupled complex short pulse equations contain the existing results as particular cases.Based on the linearizing operator and adjoint linearizing operator for the two real systems,adjoint symmetries can be obtained. Explicit conservation laws are constructed using the symmetry/adjoint symmetry pair(SA) method. Relationships between the nonlinear selfadjointness method and the SA method are investigated.

关键词： complex short pulse equation coupled complex short pulse equations symmetries adjoint symmetries conservation laws SA method

A Wavelet-Free Approach for Multiresolution-Based Grid Adaptation for conservation laws

在线全文

学校读者我要写书评

暂无评论

Communications on Applied Mathematics and Computation 2022年第1期4卷 108-142页

作者： Nils Gerhard Siegfried Müller Aleksey Sikstel Institut für Geometrie und Praktische Mathematik RWTH AachenTemplergraben 55Aachen 52056Germany

In recent years the concept of multiresolution-based adaptive discontinuous Galerkin(DG)schemes for hyperbolic conservation laws has been developed.The key idea is to perform a multiresolution analysis of the DG solution using multiwavelets defined on a hierarchy of nested grids.Typically this concept is applied to dyadic grid hierarchies where the explicit construction of the multiwavelets has to be performed only for one reference element.For non-uniform grid hierarchies multiwavelets have to be constructed for each element and,thus,becomes extremely expensive.To overcome this problem a multiresolution analysis is developed that avoids the explicit construction of multiwavelets.

关键词： Discontinuous Galerkin Grid adaptivity Multiwavelets Multiresolution analysis conservation laws

Symmetries and conservation laws associated with a hyperbolic mean curvature flow

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(A Journal of Chinese Universities) 2022年第4期37卷 583-597页

作者： GAO Ben YIN Qing-lian College of Mathematics Taiyuan University of TechnologyTaiyuan 030024China

Under investigation in this paper is a hyperbolic mean curvature flow for convex evolving curves.Firstly,in view of Lie group analysis,infinitesimal generators,symmetry groups and an optimal system of symmetries of the considered hyperbolic mean curvature flow are presented.At the same time,some group invariant solutions are computed through reduced equations.In particular,we construct explicit solutions by applying the power series method.Furthermore,the convergence of the solutions of power series is certificated.Finally,conservation laws of the hyperbolic mean curvature flow are established via Ibragimov's approach.

关键词： hyperbolic mean curvature flow symmetries power series solutions conservation laws

The Sharma-Tasso-Olver-Burgers equation:its conservation laws and kink solitons

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2022年第2期74卷 1-8页

作者： K Hosseini A Akbulut D Baleanu S Salahshour Department of Mathematics Near East University TRNCMersin 10Turkey Department of Mathematics-Computer Art-Science FacultyEskisehir Osmangazi UniversityEskisehirTurkey Department of Mathematics Faculty of Arts and SciencesCankaya UniversityAnkara 06530Turkey Institute of Space Sciences Magurele-BucharestRomania Faculty of Engineering and Natural Sciences Bahcesehir UniversityIstanbulTurkey

The present paper deals with the Sharma-Tasso-Olver-Burgers equation(STOBE)and its conservation laws and kink solitons.More precisely,the formal Lagrangian,Lie symmetries,and adjoint equations of the STOBE are firstly constructed to retrieve its conservation laws.Kink solitons of the STOBE are then extracted through adopting a series of newly well-designed approaches such as Kudryashov and exponential methods.Diverse graphs in 2 and 3D postures are formally portrayed to reveal the dynamical features of kink solitons.According to the authors’knowledge,the outcomes of the current investigation are new and have been listed for the first time.

关键词： Sharma-Tasso-Olver-Burgers equation conservation laws Kudryashov and exponential methods kink solitons dynamical features

Lump,its interaction phenomena and conservation laws to a nonlinear mathematical model

在线全文

学校读者我要写书评

暂无评论

Journal of Ocean Engineering and Science 2022年第4期7卷 363-371页

作者： Abdullahi Yusuf Tukur Abdulkadir Sulaiman Evren Hincal Dumitru Baleanu Department of Computer Engineering Biruni UniversityIstanbulTurkey Department of Mathematics Near East University TRNCMersin 10Turkey Department of Mathematics Federal University DutseJigawaNigeria Department of Mathematics Cankaya UniversityAnkaraTurkey Institute of Space Sciences MagureleBucharestRomania Department of Medical Research China Medical University HospitalChina Medical UniversityTaichungTaiwan

We solve the Ostrovsky equation in the absence of the rotation effect using the Hirota bilinear method and symbolic calculation.Some unique interaction phenomena have been obtained between lump so-lution,breather wave,periodic wave,kink soliton,and two-wave solutions.All the obtained solutions are validated by putting them into the original problem using the Wolfram Mathematica 12.The physical characteristics of the solutions have been visually represented to shed additional light on the acquired re-sults.Furthermore,using the novel conservation theory,the conserved vectors of the governing equation have been generated.The discovered results are helpful in understanding particular physical phenomena in fluid dynamics as well as the dynamics of nonlinear higher dimensional wave fields in computational physics and ocean engineering and related disciplines.

关键词： Lump solution New interaction phenomena Breather waves Symmetry analysis conservation laws

New conservation laws and exact solutions of the special case of the fifth-order KdV equation

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Ocean Engineering and Science 2022年第4期7卷 377-382页

作者： Arzu Akbulut Melike Kaplan Mohammed K.A.Kaabar Department of Mathematics-Computer Art-Science FacultyEskisehir Osmangazi UniversityEskisehirTurkey Department of Mathematics Art-Science FacultyKastamonu UniversityKastamonuTurkey Institute of Mathematical Sciences Faculty of ScienceUniversity of MalayaKuala Lumpur 50603Malaysia

The current study deals with the Kaup-Kupershmidt(KK)equation to construct formal Lagrangian,con-servation laws,and exact solutions.KK is basically a special case of the 5th-order KdV equation.The conservation laws obtained by using the conservation theorem are trivial conservation laws.In addition,exact solutions are found via the modified simple equation(MSE)method.For a suitable value of solu-tions,the 3D surfaces have been plotted using MAPLE.These plots giving novel exact solutions are made to reveal important wave characteristics.Our obtained results in this work concerning our investigated equation are essential to explain many physical and oceanographic applications involving ocean gravity waves and many other related phenomena.

关键词： conservation laws Exact solutions Symbolic computation Modified simple equation method

Breather waves, analytical solutions and conservation laws using Lie–Bäcklund symmetries to the (2 + 1)-dimensional Chaffee–Infante equation

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Ocean Engineering and Science 2023年第2期8卷 145-151页

作者： Abdullahi Yusuf Tukur Abdulkadir Sulaiman Alrazi Abdeljabbar Marwan Alquran Department of Computer Engineering Biruni University IstanbulTurkey Faculty of Science Federal University DutseJigawaNigeria Department of Mathematics Khalifa University for Science and TechnologyAbu DhabiUAE Department of Mathematics and Statistics Jordan University of Science and TechnologyIrbidJordan

The(2+1)-dimensional Chaffee–Infante has a wide range of applications in science and engineering,including nonlinear fiber optics,electromagnetic field waves,signal processing through optical fibers,plasma physics,coastal engineering,fluid dynamics and is particularly useful for modeling ion-acoustic waves in plasma and sound waves.In this paper,this equation is investigated and analyzed using two effective schemes.The well-known tanh-coth and sine-cosine function schemes are employed to establish analytical solutions for the equation under consideration.The breather wave solutions are derived using the Cole–Hopf transformation.In addition,by means of new conservation theorem,we construct conservation laws(CLs)for the governing equation by means of Lie–Bäcklund symmetries.The novel characteristics for the(2+1)-dimensional Chaffee–Infante equation obtained in this work can be of great importance in nonlinear sciences and ocean engineering.

关键词： Extended tanh-coth method Sine-cosine function method Soliton solutions Breather wave solutions conservation laws