共查询到19条相似文献,搜索用时 46 毫秒
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鉴于R iem ann积分对区间的分割和取点的双重任意性要求给应用带来的困难,本文中我们将选择“等距分割”这种特殊的分割方式来定义函数的可积性,即所谓“等分可积”.从表面上看,等分可积性要弱于R iem ann可积性,但本文将证明这两种可积性是等价的.文中还给出了等分可积准则. 相似文献
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我们给出每个绝对Henstock可积函数都是Mcshane可积的一个新的证明。 相似文献
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一致可积函数的非标准刻画 总被引:2,自引:1,他引:1
设(X,A,μ)是内有限可加测度空间.首先给出了S-可积的等价条件,进而给出了一致可积函数的非标准刻画,即可测函数集{fi)i∈I是一致可积的当且仅当对于任意的i∈*I,fi都是S-可积的. 相似文献
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Riccati微分方程的可积条件 总被引:6,自引:1,他引:5
In1998,ZhaoLinlong[1]obtainedtheintegrablecondition:R=1αγPe2∫(Q-βD)dx (α,β,γisconst).(1)ForRiccatiequation:y′=p(x)y2+Q(x)y+R(x) (PR≠0).(2) Herethenewintegrableconditionsisgiven:L[y0]=1αγPe2∫(Q+2y0p-βD)dx.(3)L[AB+y0]=1αγ(AB)2L[y0]e2∫(2BAL[y0]+Q+2y… 相似文献
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一个新的无限维Liouville可积系及其变换 总被引:7,自引:1,他引:6
徐西祥 《高校应用数学学报(A辑)》1997,(2):139-146
本文讨论了一个新的等谱特征问题,按屠规彰格式导出了相应的Lax可积的非线性发展方程族。证明了它是Liouville可积系,并且讨论了谱参数改变符号时相应的可积系的变化情况。 相似文献
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设(T(t)t〉0为Banach空间X上的局部可积半群,我们讨论(T(t)t〉0与它的多值生成元A之间的谱关系。 相似文献
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We construct integrable pseudopotentials with an arbitrary number of fields in terms of an elliptic generalization of hypergeometric
functions in several variables. These pseudopotentials are multiparameter deformations of ones constructed by Krichever in
studying the Whitham-averaged solutions of the KP equation and yield new integrable (2+1)-dimensional systems of hydrodynamic type. Moreover, an interesting class of integrable (1+1)-dimensional systems described in terms of solutions of an elliptic generalization of the Gibbons-Tsarev system is related
to these pseudopotentials. 相似文献
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We propose a method for constructing integrable lattices starting from dynamic systems with two different parameterizations of the canonical variables and hence two independent Bäcklund flows. We construct integrable lattices corresponding to generalizations of the nonlinear Schrödinger equation. We discuss the Toda, Volterra, and Heisenberg models in detail. For these systems, as well as for the Landau-Lifshitz model, we obtain totally discrete Lagrangians. We also discuss the relation of these systems to the Hirota equations. 相似文献
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R. Hernández Heredero 《Theoretical and Mathematical Physics》2002,133(2):1516-1528
We develop a classification scheme for integrable third-order scalar evolution equations using the symmetry approach to integrability. We use this scheme to study quasilinear equations of a particular type and prove that several equations that were suspected to be integrable can be reduced to the well-known Korteweg–de Vries and Krichever–Novikov equations via a Miura-type differential substitution. 相似文献
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In this paper, we aim to construct the Darboux transformation and explicit solutions for an integrable lattice introduced by Suris. Analysis of properties of the solutions shows that the obtained explicit solutions for this discrete integrable system possess new dynamical characters which are different from the ones of continuous integrable systems. 相似文献
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We construct integrable pseudopotentials with an arbitrary number of fields in terms of generalized hypergeometric functions.
These pseudopotentials yield some integrable (2 + 1)-dimensional hydrodynamic type systems. In two particular cases these
systems are equivalent to integrable scalar 3-dimensional equations of second order. An interesting class of integrable (1 + 1)-dimensional
hydrodynamic type systems is also generated by our pseudopotentials. 相似文献
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Eva Miranda 《Central European Journal of Mathematics》2014,12(2):240-270
The main purpose of this paper is to present in a unified approach to different results concerning group actions and integrable systems in symplectic, Poisson and contact manifolds. Rigidity problems for integrable systems in these manifolds will be explored from this perspective. 相似文献
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张玉峰 《数学物理学报(A辑)》2005,25(1):1-10
构造了Loop代数~A_{-1}的一个子代数,利用屠格式导出了一族新的可积孤子方程族,并且是Liouville可积系,具有双Hamilton结构。 相似文献