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Chengming Bai 《代数通讯》2013,41(3):1016-1057
Left-symmetric algebras have close relations with many important fields in mathematics and mathematical physics. Their classification is very complicated due to the nonassociativity. In this article, we re-study the correspondence between left-symmetric algebras and the bijective 1-cocycles. Then a procedure is provided to classify left-symmetric algebras in terms of classification of equivalent classes of bijective 1-cocycles. As an example, the 3-dimensional complex left-symmetric algebras are classified. 相似文献
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本文利用二项式残数表示方法生成(2+1)-维超可积系统. 由这些系统得到了一个新的(2+1)-维超孤子族,它能约化为(2+1)-维超非线性Schrodinger方程. 特别地,我们得到两个具有重要物理应用的结果,一个是(2+1)-维超可积耦合方程,另一个是(2+1)-维的扩散方程. 最后借助超迹恒等式给出了新(2+1)-维超可积系统的Hamilton结构. 相似文献
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利用等变活动标架理论,研究(2+1)-维破裂孤子方程的群叶状方法和显式解.原方程的对称群的无穷维部分被用来产生整个解空间的叶状结构,于是分解系统就继承了对称群的有限维部分.求解的过程完全符号化和算法化.利用群叶状方法,破裂孤子方程的一些显式精确解被得到,这些解关于无穷维对称子群封闭. 相似文献
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Shen Shoufeng 《高校应用数学学报(英文版)》2007,22(2)
Lie point symmetries associated with the new (2 l)-dimensional KdV equation ut 3uxuy uxxy = 0 are investigated. Some similarity reductions are derived by solving the the soliton solution is obtained directly from the B(a)cklund transformation. 相似文献
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利用一个广义等谱问题的相容性得到了一个广义零曲率方程.作为其应用,首先利用loop代数设计了两个广义等谱问题,然后利用零曲率方程导出了两类(2+1)维Lax可积系统. 相似文献
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Group-Invariant Solutions and Conservation Laws of One-Dimensional Nonlinear Wave Equation
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Ben Yang Yunjia Song Yanzhi M Xinxue Zhang 《Journal of Nonlinear Modeling and Analysis》2023,5(4):708-719
Based on classical Lie symmetry method, the one-dimensional nonlinear wave equation is investigated. By using four-dimensional subalgebras of the equation, the invariant groups and commutator table are constructed. Furthermore, optimal system of the equation is obtained, and the exact solutions can be gained by solving reduced equations. Finally, a complete derivation of the conservation law is given by using conservation multipliers. 相似文献
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K. P. Kokhas´ 《Functional Analysis and Its Applications》2002,36(3):236-239
For a field F that is the direct limit of an increasing chain of finite fields, we describe the Bratteli diagram, the finite complex factor representations, the Plancherel formula, and the projective modules of the corresponding Heisenberg group. 相似文献
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利用一种改进的统一代数方法将构造(2+1)维ZK MEW((2+1)-dimensionalZakharov-Kuznetsovmodifiedequalwidth)方程精确行波解的问题转化为求解一组非线性的代数方程组.再借助于符号计算系统Mathematica求解所得到的非线性代数方程组,最终获得了方程的多种形式的精确行波解.其中包括有理解,三角函数解,双曲函数解,双周期Jacobi椭圆函数解,双周期Weierstrass椭圆形式解等.并给出了部分解的图形. 相似文献
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KdV-Burgers方程的对称与孤子解 总被引:1,自引:0,他引:1
考虑KdV-Burgers方程的一些简单对称及其构成的李代数,并利用对称约化方法将KdV-Burgers方程化为常微分方程,从而得到该方程的群不变解.此外,利用多项式展开式的方法去获得KdV-Burgers方程的新的孤子波解. 相似文献
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Huanhe Dong 《高等学校计算数学学报(英文版)》2007,16(2):147-154
Under the frame of the (2 1)-dimensional zero curvature equation and Tu model, the (2 1)-dimensional dispersive long wave hierarchy is obtained. Furthermore, the loop algebra is expanded into a larger one. Moreover, a class of integrable coupling system for dispersive long wave hierarchy and (2 1)-dimensional multi-component integrable system will be investigated. 相似文献
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Symmetries in (1+1)-dimensional Integrable System with Their Algebraic Structures and Conserved Quantities
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In this paper we offer a general method or constructing symmetries and conserved quantities in the (1 + 1)-dimensional integrable system, prove the algebraic relations between symmetries, and what is more, give applications of this method in many integrable systems with physical significance. 相似文献
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马正义 《数学的实践与认识》2005,35(12):170-173
对于(2+1)维非线性物理模型,欲获其解并非易事.本文试图在变量分离法中,通过设定的R iccati方程来得到方程的解.同时,以(2+1)维Bo iti-L eon-M anna-P em p inelli方程和Burgers方程为例来说明之. 相似文献
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R. Campoamor-Stursberg 《Communications in Nonlinear Science & Numerical Simulation》2012,17(3):1178-1193
We complete the analysis of the symmetry algebra L for systems of n second-order linear ODEs with constant real coefficients, by studying the case of coefficient matrices having a non-diagonal Jordan canonical form. We also classify the Levi factor (maximal semisimple subalgebra) of L, showing that it is completely determined by the Jordan form. A universal formula for the dimension of the symmetry algebra of such systems is given. As application, the case n = 5 is analyzed. 相似文献
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Lie point symmetries associated with the new (2 1)-dimensional KdV equation ut 3uxuy uxxy= 0 are investigated. Some similarity reductions are derived by solving the corresponding characteristic equations. Painleve analysis for this equation is also presented and the soliton solution is obtained directly from the Backlund transformation. 相似文献
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M. Nadjafikhah R. Bakhshandeh-Chamazkoti A. Mahdipour-Shirayeh 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5164-5169
In this paper, a symmetry classification of a (2+1)-nonlinear wave equation utt−f(u)(uxx+uyy)=0 where f(u) is a smooth function on u, using Lie group method, is given. The basic infinitesimal method for calculating symmetry groups is presented, and used to determine the general symmetry group of this (2+1)-nonlinear wave equation. 相似文献