Davey-Stewartson系统粗糙爆破解的极限行为

研究了Davey-Stewartson系统(简记为D-S系统)粗糙爆破解的动力学性质.所谓粗糙爆破解即为正则性为H~s(s1)的爆破解,此时D-S系统粗糙解不再满足能量守恒率.利用I-方法与Profile分解理论,得到了D-S系统粗糙爆破解在H~s(R~2)(其中ss_0,且s_0≤(1+11~(1/2))/5≈0.8633)中的极限行为,包括L~2强极限的不存在性与L~2集中性质以及极限图景.     

The sharp threshold and limiting profile of blow-up solutions for a Davey-Stewartson system

The blow-up solutions of the Cauchy problem for the Davey-Stewartson system, which is a model equation in the theory of shallow water waves, are investigated. Firstly, the existence of the ground state for the system derives the best constant of a Gagliardo-Nirenberg type inequality and the variational character of the ground state. Secondly, the blow-up threshold of the Davey-Stewartson system is developed in R³. Thirdly, the mass concentration is established for all the blow-up solutions of the system in R². Finally, the existence of the minimal blow-up solutions in R² is constructed by using the pseudo-conformal invariance. The profile of the minimal blow-up solutions as t→T (blow-up time) is in detail investigated in terms of the ground state.     

ILL-POSEDNESS FOR THE NONLINEAR DAVEY-STEWARTSON EQUATION

The nonlinear D-S equations on R^d, with general power nonlinearity and with both the focusing and defocusing signs, are proved to be ill-posed in the Sobolev space H^s whenever the exponent s is lower than that predicted by scaling or Galilean invariance, or when the regularity is too low to support distributional solutions. Authors analyze a class of solutions for which the zero-dispersion limit provides good approximations.     

EXISTENCE AND DECAY OF WEAK SOLUTIONS TO DEGENERATE DAVEY-STEWARTSON EQUATIONS

In this paper, the authors consider a system of degenerate Davey-Stewartson equations. They prove the global existence of weak solutions in some weighted function spaces and the decay of weak solutions in some anisotropic spaces for appropriate initial data.     

三维空间中广义Davey-Stewartson系统整体解

根据基态的特征,用势井方法和凹方法证明了三维空间中广义Davey-Stewartson 系统解爆破和整体存在的最佳条件.同时还证明了当初值为多小时,该系统的整体解存在     

Dromion solutions for an electron acoustic wave and its application to space observations

The nonlinear evolution of an electron acoustic wave is shown to obey the Davey-Stewartson I equation which admits so called dromion solutions. The importance of these two dimensional localized solutions for recent satellite observations of wave structures in the day side polar cap regions is discussed and the parameter regimes for their existence is delineated.     

Davey-Stewartson方程组的包络周期解和孤立波解

应用Jacobi椭圆函数展开法,求得了Davey-Stewartson方程组的包络周期解和孤立波解． 关键词： Davey-Stewartson方程 Jacobi椭圆函数 包络周期解 孤立波解     

广义Davey-Stewartson系统驻波的强不稳定性

本文研究方程驻波的强不稳定性iu_t+△u+a|u|~(p-1)u+E_1(|u|~2)u=0,t≥0,x∈R~n,其中a0,1p(n+2)/(n+2)~+,n∈{2,3}.当1+4/n≤pn+2/(n-2)~+)时,文[Sharp threshold of global existence and instability of standing wave for a Davey-Stewartson system,Commun.Math.Phys.,2008,283:93-125]在驻波的频率满足一定假设条件下,证明了此方程驻波的强不稳定性.本文去掉这个假设,得到相同的结论.     

Exact Dark Soliton and Its Persistence in the Perturbed2+1-dimensional Davey-Stewartson System

For the Davey-Stewartson system, the exact dark solitary wave solutions, solitary wave solutions, kink wave solution and periodic wave solutions are studied. To guarantee the existence of the above solutions, all parameter conditions are determined. The persistence of dark solitary wave solutions to the perturbed Davey-Stewartson system is proved.