共查询到20条相似文献,搜索用时 62 毫秒
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给出了包含宏观应变和微形变的全部二次项以及宏观应变三次项的一种新的自由能函数.利用新自由能函数并根据Mindlin微结构理论,建立了描述微结构固体中纵波传播的一种新模型.利用近来发展的奇行波系统的动力系统理论,分析了系统的所有相图分支,并给出了周期波解、孤立波解、准孤立尖波解、孤立尖波解以及紧孤立波解.孤立尖波解和紧孤立波解的得到,有效地证明了在一定条件下,微结构固体中可以形成和存在孤立尖波和紧孤立波等非光滑孤立波.此结果进一步推广了微结构固体中只存在光滑孤立波的已有结论. 相似文献
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Degasperis-Procesi方程的孤立尖波解 总被引:1,自引:0,他引:1
利用动力系统的定性分析理论对D egasperis-P rocesi方程的孤立尖波解进行了研究.给出了D e-gasperis-P rocesi方程对应行波系统的相图分支,利用相图获得了孤立尖波解和周期尖波解的解析表达式,通过数值模拟给出了部分解的图像. 相似文献
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运用平面动力系统的分支方法,研究了一类非线性方程的行波解,画出了在不同参数条件下的相图,证明方程存在周期行波解和周期尖波解.给出了有界波的精确的参数表达式,指出了周期尖波是周期波的极限形式,同时指出了方程不存在圈孤子解. 相似文献
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本文利用动力系统方法和奇行波方程理论研究广义Gilson-Pickering方程的动力学行为和行波解.利用软件画出了给定参数条件下系统的相图分支,得到了孤立波解、扭结波解和反扭结波解、不可数无穷多破缺波解、光滑周期波解和非光滑周期尖波解、尖孤子解的存在性.在β≠1,p=2时,对于广义Gilson-Pickering方程不同的参数条件下,给出了保证上述解存在的条件及参数表示. 相似文献
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杨海霞 《纯粹数学与应用数学》2013,(3):306-317
构造一个组合方程的单孤子解和周期尖波解.应用格林函数的性质,以及求一个非线性偏微分方程(简称PDE)弱解的方法.求出了这个组合方程的单孤子解和周期尖波解,推广了前人的研究成果. 相似文献
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带色散项的Degasperis-Procesi方程的孤立尖波解 总被引:2,自引:0,他引:2
用动力系统的定性分析理论研究了带有色散项的Degasperis-Procesi方程的孤立尖波解.在一定的参数条件下,利用Degasperis-Procesi方程对应行波系统的相图分支从两种不同方式给出了孤立尖波解的表达式. 相似文献
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Lax形式的5阶KdV方程的尖孤波解尚未见有文献报道.本文首次给出Lax形式的5阶KdV方程的两类尖孤波解.这两类孤波解都有尖峰或倒尖峰,且满足Rankine-Hugoniot条件和熵条件,是方程的物理解. 相似文献
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Qualitative Analysis and Periodic Cusp Waves to a
Class of Generalized Short Pulse Equations 下载免费PDF全文
In this paper, we qualitatively study periodic cusp waves to a class
of generalized short pulse equations, which are of the general form of three
special generalized short pulse equations, from the perspective of dynamical
systems. We show the existence of smooth periodic waves, periodic cusp wave
and compactons, obtain exact expression of periodic cusp wave and illustrate
the limiting process of periodic cusp wave from smooth periodic waves. 相似文献
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Min Ho Lee 《manuscripta mathematica》1991,73(1):163-177
We define the periods of mixed cusp forms and establish generalized Eichler-Shimura relations for the periods of mixed cusp
forms. We also construct modular symbols for mixed cusp forms and express the periods of mixed cusp forms in terms of these
modular symbols. 相似文献
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Kathrin Bringmann 《Mathematische Zeitschrift》2006,253(4):735-752
In this paper we construct a lifting map from a vector space of generalized Jacobi cusp forms to a certain subspace of elliptic
cusp forms and vice versa such that both mappings are adjoint with respect to the Petersson scalar products. 相似文献
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In this paper, we study some generalized Camassa-Holm equation. Through the analysis of the phase-portraits, the existence of solitary wave, cusp wave, periodic wave, periodic cusp wave and compactons were discussed. In some certain parametric conditions, many exact solutions to the above travelling waves were given. Further-more, the 3D and 2D pictures of the above travelling wave solutions are drawn using Maple software. 相似文献
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By constructing auxiliary differential equations, we obtain peaked solitary wave solutions of the generalized Camassa-Holm equation, including periodic cusp waves expressed in terms of elliptic functions. 相似文献
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Abhishek Saha 《The Ramanujan Journal》2014,33(2):263-268
We show that a weak form of the generalized Böcherer conjecture implies multiplicity one for Siegel cusp forms of degree 2. 相似文献
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The Ramanujan Journal - We study the angle changes of Fourier coefficients of cusp forms and q-exponents of generalized modular functions at primes. More precisely, we prove that both these... 相似文献
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We give congruences between the Eisenstein series and a cusp form in the cases of Siegel modular forms and Hermitian modular forms. We should emphasize that there is a relation between the existence of a prime dividing the (k?1)th generalized Bernoulli number and the existence of non-trivial Hermitian cusp forms of weight k. We will conclude by giving numerical examples for each case. 相似文献
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The Ramanujan Journal - Let $$\lambda _{f}(n)$$ be the normalized Fourier coefficients of a holomorphic Hecke cusp form of full level. We study a generalized divisor problem with $$\lambda... 相似文献
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This paper deals with a class of generalized KdV equation by making use of a mathematical technique based on using integral factors for solving differential equations and give rise to the solitary wave, periodic cusp wave and periodic wave solutions. The work confirms the power of the proposed method. 相似文献