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1.
The generalized nonlinear Schrödinger equation (GNLS) iut + uxx + βu2u + γu4u + iα (u2u)x + iτ(u2)xu = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schrödinger equation. Int J Bifucat Chaos 2005:3295–305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained. 相似文献
2.
Andrs Bir 《Finite Fields and Their Applications》2000,6(4):301
Let p>2 be a prime, denote by Fp the field with Fp=p, and let F*p=Fp\{0}. We prove that if fεFp[x] and f takes only two values on F*p, then (excluding some exceptional cases) the degree of f is at least
(p−1). 相似文献
3.
4.
Let X={X(t), t[0,1]} be a process on [0,1] and VX=Conv{(t,x)t[0,1], x=X(t)} be the convex hull of its path.The structure of the set ext(VX) of extreme points of VX is studied. For a Gaussian process X with stationary increments it is proved that:
- • The set ext(VX) is negligible if X is non-differentiable.
- • If X is absolutely continuous process and its derivative X′ is continuous but non-differentiable, then ext(VX) is also negligible and moreover it is a Cantor set.
5.
Asymptotic behavior of solutions of semilinear elliptic equations near an isolated singularity 总被引:1,自引:0,他引:1
We consider the semilinear elliptic equation Δu=h(u) in Ω{0}, where Ω is an open subset of (N2) containing the origin and h is locally Lipschitz continuous on [0,∞), positive in (0,∞). We give a complete classification of isolated singularities of positive solutions when h varies regularly at infinity of index q(1,CN) (that is, limu→∞h(λu)/h(u)=λq, for every λ>0), where CN denotes either N/(N−2) if N3 or ∞ if N=2. Our result extends a well-known theorem of Véron for the case h(u)=uq. 相似文献
6.
Nonradial large solutions of sublinear elliptic problems 总被引:1,自引:0,他引:1
Khalifa El Mabrouk Wolfhard Hansen 《Journal of Mathematical Analysis and Applications》2007,330(2):1025-1041
Let p be a nonnegative locally bounded function on , N3, and 0<γ<1. Assuming that the oscillation sup|x|=rp(x)−inf|x|=rp(x) tends to zero as r→∞ at a specified rate, it is shown that the equation Δu=p(x)uγ admits a positive solution in satisfying lim|x|→∞u(x)=∞ if and only if 相似文献
7.
Grgoire Nadin 《Journal de Mathématiques Pures et Appliquées》2009,92(3):232-262
This paper is concerned with the existence of pulsating traveling fronts for the equation:(1)
∂tu−(A(t,x)u)+q(t,x)u=f(t,x,u),