The negative extended KdV equation with self-consistent sources: soliton, positon and negaton

The negative extended KdV equation with self-consistent sources (eKdV⁻ESCSs) is firstly presented and the associated linear auxiliary equations are derived. The generalized binary Darboux transformation (DT) is applied to construct some new solutions of the eKdV⁻ESCSs such as singular N-soliton solution, N-soliton solution with finite amplitude, N-positon solution and N-negaton solution. The properties of these solutions are analyzed. Moreover, the interactions of two solitons, positon and negaton, positon and soliton, and two positons are discussed.     

Some remarks on Prandtl system

The purpose of this paper is to correct some drawbacks in the proof of the well-known Boundary Layer Theory in Oleinik’s book. The Prandtl system for a nonstationary layer arising in an axially symmetric incopressible flow past a solid body is analyzed. This paper was supported by NSF of China (10571144), NSF for youth of Fujian province in China (2005J037) and NSF of Jimei University in China.     

On Rectifiable Curves in the Plane

This paper gives a formula of integral for the rectifiable curves in the plane by the Hausdorff fractional derivation and integral. Received August 10, 1999, Revised December 27, 1999, Accepted January 14, 2000     

The second initial-boundary value problem for a quasilinear parabolic equations with nonlinear boundary conditions

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｆａｓｔｄｉｆｆｕｓｉｏｎｅｑｕａｔｉｏｎｏｆｄｉｖｅｒｇｅｎｃｅｆｏｒｍａｓｕｔ =(ａ(ｕ)ｕｘ) ｘ ｂ(ｕ) ｘ ｃ(ｕ)　　 (ａ( 0 ) = ∞ ) ( 1 )ｈａｓｉｍｐｏｒｔａｎｔｐｈｙｓｉｃａｌｂａｃｋｇｒｏｕｎｄ ,ｓｕｃｈａｓ [1 ] .Ｉｎｒｅｃｅｎｔｙｅａｒｓ ,ｓｏｍｅｒｅｓｕｌｔｓａｂｏｕｔ ( 1 )ｈａｖｅｂｅｅｎｏｂｔａｉｎｅｄ .Ｆｏｒｅｘａｍｐｌｅ ,[2 ] ,[3]ｒｅｓｐｅｃｔｉｖｅｌｙｄｉｓｃｕｓｓｅｄｔｈｅＣａｕｃｈｙｐｒｏｂｌｅｍｓｆｏｒｅｑｕａｔｉｏｎ( 1 )ａｎｄｕｔ=(…     

序压缩映射的不动点定理

本文在序Banach空间中引入了几种按序压缩的压缩型映射,证明了相应的不动点定理.     

非线性Kundu方程的弱守恒差分格式

本文考察了一类非线性Kundu方程的周期初值问题,提出了一种弱守恒的差分格式,对其差分解作了先验估计,证明了格式的收敛性与稳定性,最后,通过数值计算检验了格式的可信性.     

具非线性边界条件的奇异扩散方程

本文讨论具非线性第二边界条件的一端无界的奇异扩散方程的初边值间题,利用先验估计方法得到的主要结果是:存在唯一的整体光滑解,且解连续依赖于初值．     

具有脉冲效应的周期三种群捕食-食饵系统

本文讨论一类具有脉冲效应和周期系数的两个食饵一个捕食者的捕食-食饵系统的动力学行为.利用脉冲微分方程比较定理和乘子理论,证明了系统的有界性,讨论了平凡周期解和半平凡周期解的稳定性,利用重合度的理论给出了系统存在周期正解的充分条件.     

纳米ZnO胶体可见发射机制的研究

关于ZnO可见发射机制的讨论目前尚无定论。本文研究了不同颗粒尺寸的纳米晶ZnO胶体的发射性质,观测到两个发射带,其中之一是激子发射,另一个是可见发射;发现两个发射带的峰值能量之间存在线性关系,并由此提出了可见发射机制是来自导带的电子到深陷阱的跃迁。     

DYNAMICS OF A NONLINEAR NON-AUTONOMOUS n-PATCHES PREDATOR-PREY DISPERSION-DELAY MODEL

In this paper,a nonlinear nonautonomous predator-prey dispersion model with continuous distributed delay is studied,where all parameters are time-dependent.In this system consisting of n-patches the prey species can disperse among n-patches,but the predator species is confined to one patch and cannot disperse.It is proved that the system is uniformly persistent under any dispersion rate effect.Furthermore,some sufficient conditions are established for the existence of a unique almost periodic solution of the system.The example shows that the criteria in the paper are new,general and easily verifiable.