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1.
We study a two-component Novikov system, which is integrable and can be viewed as a twocomponent generalization of the Novikov equation with cubic nonlinearity. The primary goal of this paper is to understand how multi-component equations, nonlinear dispersive terms and other nonlinear terms affect the dispersive dynamics and the structure of the peaked solitons. We establish the local well-posedness of the Cauchy problem in Besov spaces B_(p,r)~s with 1 p, r +∞, s max{1 + 1/p, 3/2} and Sobolev spaces Hs(R)with s 3/2, and the method is based on the estimates for transport equations and new invariant properties of the system. Furthermore, the blow-up and wave-breaking phenomena of solutions to the Cauchy problem are studied. A blow-up criterion on solutions of the Cauchy problem is demonstrated. In addition, we show that this system admits single-peaked solitons and multi-peaked solitons on the whole line, and the single-peaked solitons on the circle, which are the weak solutions in both senses of the usual weak form and the weak Lax-pair form of the system.  相似文献   

2.
For the two-dimensional Walsh system, Gat and Weisz proved the a.e. convergence of Fejer means σnf of integrable functions, where the set of indices is inside a positive cone around the identical function, that is, β^-1≤n1/n2 ≤β is provided with some fixed parameter ~ 〉 1. In this paper we generalize the result of Gat and Weisz. We not only generalize this theorem, but give a necessary and sufficient condition for cone-like sets in order to preserve this convergence property.  相似文献   

3.
In this paper, we consider a single species non-autonomous system with pure-delay and feedback control. Sufficient conditions of integrable form for the permanence of species are established.  相似文献   

4.
In this paper we consider the persistence of invariant tori of an integrable Hamiltonian system with a quasiperiodic perturbation. It is proved that if the unperturbed system satisfies the Rtissmann non-degenerate condition and the perturbed system satisfies the co-linked non-resonant condition, then the majority of invariant tori is persistent under the perturbation.  相似文献   

5.
In this paper,we study the Cauchy problem of an integrable evolution system,i.e.,the n-dimensional generalization of third-order symmetry of the well-known Landau-Lifshitz equation.By rewriting this equation in a geometric form and applying the geometric energy method with a forth-order perturbation,we show the global well-posedness of the Cauchy problem in suitable Sobolev spaces.  相似文献   

6.
With the help of a Lie algebra,two kinds of Lie algebras with the forms of blocks are introduced for generating nonlinear integrable and bi-integrable couplings.For illustrating the application of the Lie algebras,an integrable Hamiltonian system is obtained,from which some reduced evolution equations are presented.Finally,Hamiltonian structures of nonlinear integrable and bi-integrable couplings of the integrable Hamiltonian system are furnished by applying the variational identity.The approach presented in the paper can also provide nonlinear integrable and bi-integrable couplings of other integrable system.  相似文献   

7.
We characterize the Liouvillian and analytic integrability of the quadratic polynomial vector fields in R2 having an invariant ellipse.More precisely,a quadratic system having an invariant ellipse can be written into the form x=x2+y2-1+y(ax+by+c),y=x(ax+by+c),and the ellipse becomes x2+y2=1.We prove that(i) this quadratic system is analytic integrable if and only if a=0;(ii) if x2+y2=1 is a periodic orbit,then this quadratic system is Liouvillian integrable if and only if x2+y2=1 is not a limit cycle;and(iii) if x2+y2=1 is not a periodic orbit,then this quadratic system is Liouvilian integrable if and only if a=0.  相似文献   

8.
In this paper, we consider the bifurcation for a class of cubic integrable system under cubic perturbation. Using bifurcation theory and qualitative analysis, we obtain a complete bifurcation diagram of the system in a neighbourhood of the origin for parameter plane.  相似文献   

9.
By introducing the conception "relativistic differential Galois group" for the second order polynomial systems, we establish the relation between the conformal relativistic differential Galois group and the subgroup of Mobius transformations, and prove that the system is integrable in the sense of Liouville if its conformal relativistic differential Galois group is solvable with a derived length at most 2. Some omissions on the structures of solvable subgroups of Mobius transformations at the first author's article published in this journal in 1996 are refreshed in this paper.  相似文献   

10.
By modifying the procedure of binary nonlinearization for the AKNS spectral problem and its adjoint spectral problem under an implicit symmetry constraint,we obtain a finite dimensional system from the Lax pair of the nonlinear Schr¨odinger equation.We show that this system is a completely integrable Hamiltonian system.  相似文献   

11.
The authors establish a Serrin's regularity criterion for the β-generalized dissipative surface quasi-geostrophic equation.More precisely,it is shown that if the smooth solution θ satisfies ▽θ∈L~q(0,T;L~P(R~2)) with α/q+2/p≤α+β-1,then the solution θcan be smoothly extended after time T.In particular,when α+β≥2,it is shown that if α_yθ∈L~q(0,T;L~P(R~2)) with α/q+2/p≤α+β-1,then the solution θ can also be smoothly extended after time T.This result extends the regularity result of Yamazaki in 2012.  相似文献   

12.
The purpose of the paper is to study sharp weak-type bounds for functions of bounded mean oscillation. Let 0 p ∞ be a fixed number and let I be an interval contained in R. The author shows that for any φ : I → R and any subset E I of positive measure,For each p, the constant on the right-hand side is the best possible. The proof rests on the explicit evaluation of the associated Bellman function. The result is a complement of the earlier works of Slavin, Vasyunin and Volberg concerning weak-type, L ~p and exponential bounds for the BMO class.  相似文献   

13.
Let P(G,λ) be the chromatic polynomial of a simple graph G. A graph G is chromatically unique if for any simple graph H, P(H,λ) = P(G,λ) implies that H is isomorphic to G. Many sufficient conditions guaranteeing that some certain complete tripartite graphs are chromatically unique were obtained by many scholars. Especially, in 2003, Zou Hui-wen showed that if n 31m2 + 31k2 + 31mk+ 31m? 31k+ 32√m2 + k2 + mk, where n,k and m are non-negative integers, then the complete tripartite graph K(n - m,n,n + k) is chromatically unique (or simply χ-unique). In this paper, we prove that for any non-negative integers n,m and k, where m ≥ 2 and k ≥ 0, if n ≥ 31m2 + 31k2 + 31mk + 31m - 31k + 43, then the complete tripartite graph K(n - m,n,n + k) is χ-unique, which is an improvement on Zou Hui-wen's result in the case m ≥ 2 and k ≥ 0. Furthermore, we present a related conjecture.  相似文献   

14.
Let and be bounded linear operators on a Hilbert space satisfying . The well-known Furuta inequality is given as follows: Let and ; then . In order to give a self-contained proof of it, Furuta (1989) proved that if , and , then .

This paper aims to show a sharpening of Furuta (1989): Let , and ; then . We call it the complete form of Furuta inequality because the case of it implies the essential part () of Furuta inequality for by the famous Löwner-Heinz inequality. Afterwards, the optimality of the outer exponent of the complete form is considered. Lastly, we give some applications of the complete form to Aluthge transformation.

  相似文献   


15.
Let T_σ be the bilinear Fourier multiplier operator with associated multiplier σ satisfying the Sobolev regularity that sup κ∈Z∥σ_κ∥W~s(R~(2n)) ∞ for some s ∈ (n, 2n]. In this paper, it is proved that the commutator generated by T_σ and CMO(R~n) functions is a compact operator from L~(p1)(R~n, w_1) × L~(p2)(R~n, w_2) to L~p(R~n, ν_w) for appropriate indices p_1, p_2, p ∈ (1, ∞) with1 p=1/ p_1 +1/ p_2 and weights w_1, w_2 such that w = (w_1, w_2) ∈ A_(p/t)(R~(2n)).  相似文献   

16.
根据速度的水平分量$u_h$的垂直导数,本文研究了3维液晶方程的整体正则性,具体地,当速度的水平分量$u_h$的垂直导数满足$\partial_3u_h\in L^p(0,T; R^3), \frac{2}{p}+\frac{3}{q}\le \frac{3}{2}$, $2\le p\le \infty$,则局部强解$(u,d)$可以光滑的延拓出$t=T$.  相似文献   

17.
In this paper, we study the asymptotic behavior of solutions to a quasilinear fully parabolic chemotaxis system with indirect signal production and logistic sourceunder homogeneous Neumann boundary conditions in a smooth bounded domain $Ω⊂\mathbb{R}^n$ $(n ≥1)$, where $b ≥0$, $γ ≥1$, $a_i ≥1$, $µ$, $b_i >0$ $(i =1,2)$, $D$, $S∈ C^2([0,∞))$ fulfilling $D(s) ≥ a_0(s+1)^{−α}$, $0 ≤ S(s) ≤ b_0(s+1)^β$ for all $s ≥ 0,$ where $a_0,b_0 > 0$ and $α,β ∈ \mathbb{R}$ are constants. The purpose of this paper is to prove that if $b ≥ 0$ and $µ > 0$ sufficiently large, the globally bounded solution $(u,v,w)$ with nonnegative initial data $(u_0,v_0,w_0)$ satisfies $$\Big\| u(·,t)− \Big(\frac{b}{µ}\Big)^{\frac{1}{γ}}\Big\|_{L^∞(Ω)}+\Big\| v(·,t)−\frac{b_1b_2}{a_1a_2}\Big(\frac{b}{µ}\Big)^{\frac{1}{γ}}\Big\| _{L^∞(Ω)} +\Big\| w(·,t)−\frac{b_2}{a_2}\Big(\frac{b}{µ}\Big)^{\frac{1}{γ}}\Big\| _{L^∞(Ω)}→0$$ as $t→∞$.  相似文献   

18.
研究了$(n+p)$维双曲空间$\mathbb{H}^{n+p}$中完备非紧子流形的第一特征值的上界.特别地,证明了$\mathbb{H}^{n+p}$中具有平行平均曲率向量$H$和无迹第二基本形式有限$L^q(q\geq n)$范数的完备子流形的第一特征值不超过$\frac{(n-1)^2(1-|H|^2)}{4}$,和$\mathbb{H}^{n+1}(n\leq5)$中具有常平均曲率向量$H$和无迹第二基本形式有限$L^q(2(1-\sqrt{\frac{2}{n}})相似文献   

19.
20.
本文在无边界流的光滑有界区域$\Omega\subset\mathbb{R}^n~(n>2)$上研究了具有奇异灵敏度及logistic源的抛物-椭圆趋化系统$$\left\{\begin{array}{ll}u_t=\Delta u-\chi\nabla\cdot(\frac{u}{v}\nabla v)+r u-\mu u^k,&x\in\Omega,\,t>0,\\ 0=\Delta v-v+u,&x\in\Omega,\,t>0\end{array}\right.$$ 其中$\chi$, $r$, $\mu>0$, $k\geq2$. 证明了若当$r$适当大, 则当$t\rightarrow\infty$时该趋化系统全局有界解呈指数收敛于$((\frac{r}{\mu})^{\frac{1}{k-1}}, (\frac{r}{\mu})^{\frac{1}{k-1}})$.  相似文献   

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