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1.
Cauchy problem for the Zakharov System Arising from Ion-Acoustic Modes with low regularity data
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We prove local well-posedness results for the Zakharov System Arising from Ion-Acoustic Modes in two spacial dimension with large initial data in low regularity Sobolev space \( (\dot{H}^1 \bigcup H^{\frac{1}{2}})\times L^2 \times H^{-1} \). Using ”derivative sharing”, the local well-posedness results in \( (\dot{H}^1 \bigcup H^{\frac{1}{2}-\delta})\times H^{\delta} \times H^{-1+\delta}\) are also obtained, for any 0 \(\leq \delta \leq 1/2 \). 相似文献
2.
On the integrability of the differential systems in dimension two and of the polynomial differential systems in arbitrary dimension
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Jaume Llibre 《Journal of Applied Analysis & Computation》2011,1(1):33-52
This is a survey on recent results providing sufficient conditions for the existence of a first integral, first for vector fields defined on real surfaces, and second for polynomial vector fields in \(R^n\) or \(C^n\) with \(n\geq 2\). We also provide an open question and some applications based on the existence of such first integrals. 相似文献
3.
Periodica Mathematica Hungarica - In this paper we find all positive integer solutions (x, y, n, a, b) of the equation in the title for non negative integers a... 相似文献
4.
Results in Mathematics - Given a self-adjoint second order differential operator L with positive characteristic and subellipticity of order 1 ≤ τ < 2.... 相似文献
5.
In this paper, we consider the stability of equilibria, Hopf and double Hopf bifurcation in Liu system with delay feedback. Firstly, we identify the critical values for stability switches and Hopf bifurcationusing the method of bifurcation analysis. When we choose appropriate feedback strength and delay, two symmetrical nontrivial equilibria of Liusystem can be controlled to be stable at the same time, and the stable bifurcating periodic solutions occur in the neighborhood of the two equilibria at the same time. Secondly, by applying the normal form method and center manifold theory,the normal form near the double Hopf bifurcation, as well as classifications of local dynamics are analyzed. Furthermore, we give the bifurcation diagram to illustrate numerically that a family of stable periodic solutions bifurcated from Hopf bifurcation occur in a large region of delay and the Liu system with delay can appear the phenomenon of ``chaos switchover''. 相似文献
6.
Positivity - This paper deals with (1, 1; r)-convexity of sequences. First, we prove several results on the sets of (1, 1; r)-convex sequences for various values... 相似文献
7.
Queueing Systems - In this paper, we investigate exact tail asymptotics for the stationary distribution of a fluid model driven by the M / M / c queue, which is... 相似文献
8.
Queueing Systems - We study the occurrence of large queue lengths in the GI / GI / d queue with heavy-tailed Weibull-type service times. Our analysis hinges on a... 相似文献
9.
Existence of Generalized Traveling Waves in Time Recurrent and Space Periodic Monostable Equations
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Wenxian Shen 《Journal of Applied Analysis & Computation》2011,1(1):69-94
This paper is concerned with the extension of the concepts and theories of traveling wave solutions of time and space periodic monostable equations to time recurrent and space periodic ones. It first introduces the concept of generalized traveling wave solutions of time recurrent and space periodic monostable equations, which extends the concept of periodic traveling wave solutions of time and space periodic monostable equations to time recurrent and space periodic ones. It then proves that in the direction of any unit vector \(\xi\), there is \(c^*(\xi)\) such that for any \(c>c^*(\xi)\), a generalized traveling wave solution in the direction of \(\xi\) with averaged propagation speed \(c\) exists. It also proves that if the time recurrent and space periodic monostable equation is indeed time periodic, then \(c^*(\xi)\) is the minimal wave speed in the direction of \(\xi\) and the generalized traveling wave solution in the direction of \(\xi\) with averaged speed \(c>c^*(\xi)\) is a periodic traveling wave solution with speed \(c\), which recovers the existing results on the existence of periodic traveling wave solutions in the direction of \(\xi\) with speed greater than the minimal speed in that direction. 相似文献
10.
Designs, Codes and Cryptography - Given an integer $$k\ge 3$$ and a group G of odd order, if there exists a 2-(v, k, 1)-design and if v is sufficiently large then there... 相似文献
11.
Bifurcation of limit cycles and isochronous center at infinity for a class of differential systems
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In this paper, we study a seventh degree polynomial differential system with full linear terms and cubic terms. The conditions of infinity to be a center and to be a fine focus of the highestorder are given and it is proved that this system has eight limit cycles in the neighborhood of infinity. Moreover, the conditions of infinity to be an isochronous center for a rational system associated the seventh degree polynomial differential system are obtained. 相似文献
12.
Semigroup Forum - A binary operation f(x, y) is said to be lazy if every operation that can be obtained from f by composition is equivalent to f(x, y), f(x, x) or x. We... 相似文献
13.
In this paper we consider the most general system proposed to describe the thermoviscoelasticity with voids. We study two qualitative properties of the solutions of this theory. First, we obtain a uniqueness result when we do not assume any sign to the internal energy. Second we extend some previous results and prove the analyticity of the solutions. The impossibility of localization in time of the solutions is a consequence. Last result we present corresponds to the analyticity of solutions in case that the dissipation is not very strong, but with suitable coupling terms. 相似文献
14.
The Ramanujan Journal - We observe that $$(F(n+k+1,k)+G(n+k,k), G(n+k,k))$$ is a WZ pair provided that (F(n, k), G(n, k)) is a WZ pair. This observation enables us to... 相似文献
15.
Explicit soliton solutions of the Kaup-Kupershmidt equation through the dynamical system approach
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In this paper, we study the traveling wave solutions of the Kaup-Kupershmidt (KK) equation through using the dynamical system approach, which is an integrable fifth-order wave equation. Based on Cosgrove's work [3] and the phase analysis method of dynamical systems, infinitely many soliton solutions are presented in an explicit form. To guarantee the existence of soliton solutions, we discuss the parameters range as well as geometrical explanation of soliton solutions. 相似文献
16.
Siberian Mathematical Journal - A frequency $ n $ -cube F $ {}^{n}(4;2,2) $ is an $ n $ -dimensional $ 4 $ -by-…-by- $ 4 $ array filled by $ 0 $ s and $ 1 $ s... 相似文献
17.
\( {\small \bf Communication Letter:}\) Four limit cycles in quadratic near-integrable system
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In this note, we report of obtaining 4 limit cycles in quadratic near-integrable polynomial systems. It is shown that when a quadratic integrable system has two centers and is perturbed by quadratic polynomials, it can generate at least 4 limit cycles with (3.1) distribution. This result provides a positive answer to an open problem in this area. 相似文献
18.
In this paper, we consider a lattice system of stochastic Zakharov equation with white noise. We first show that the solutions of the system determine a continuous random dynamical system with random absorbing set. And then we prove the random asymptotic compact on the random absorbing set. Finally, we obtain the existence of a random attractor for the system. 相似文献
19.
Bifurcation of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems of degree 5 with a cusp
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This paper deals with small perturbations of a class of hyper-elliptic Hamiltonian system, which is a Li é nard system of the form \(\dot{x}=y,\) \(\;\dot{y}=Q_1(x)+\varepsilon yQ_2(x)\) with \(Q_1\) and \(Q_2\) polynomials of degree 4 and 3, respectively. It is shown that this system can undergo degenerated Hopf bifurcation and Poincar é bifurcation, which emerge at most three limit cycles for \(\varepsilon\) sufficiently small. 相似文献
20.
The extended tanh-coth method and sech method are used to construct exact solutions of a new coupled ZK system. Traveling wave solutions are determined, which include solitary wave and periodic wave solutions. 相似文献