In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schr6dinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schr6dinger-Boussinesq equat...In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schr6dinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schr6dinger-Boussinesq equations are shown to have new the parametric representations of peakon, cuspon, smooth solRon and periodic cusp wave solutions. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are g/van.展开更多
This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N ≥ 2. We address the question of well-posedness for large data having critical Besov regularity. Our result improves N the...This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N ≥ 2. We address the question of well-posedness for large data having critical Besov regularity. Our result improves N the analysis of Danchin and of the author inasmuch as we may take initial density in BN/p p,1 with 1 ≤ p 〈 ＋∞. Our result relies on a new a priori estimate for the velocity, where we introduce a new unknown called effective velocity to weaken one of the couplings between the density and the velocity. In particular, our result is the first in which we obtain uniqueness without imposing hypothesis on the gradient of the density.展开更多
In this paper, we study the dynamics of a diffusive modified Leslie-Cower model with the multiplicative Allee effect and Ba^zykin functional response. We give detailed study on the stability of equilibria. Non-existen...In this paper, we study the dynamics of a diffusive modified Leslie-Cower model with the multiplicative Allee effect and Ba^zykin functional response. We give detailed study on the stability of equilibria. Non-existence of non-constant positive steady state solutions are shown to identify the rage of parameters of spatial pattern formation. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos.11361017,11161013Natural Science Foundation of Guangxi under Grant Nos.2012GXNSFAA053003,2013GXNSFAA019010Program for Innovative Research Team of Guilin University of Electronic Technology
文摘In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schr6dinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schr6dinger-Boussinesq equations are shown to have new the parametric representations of peakon, cuspon, smooth solRon and periodic cusp wave solutions. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are g/van.
文摘This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N ≥ 2. We address the question of well-posedness for large data having critical Besov regularity. Our result improves N the analysis of Danchin and of the author inasmuch as we may take initial density in BN/p p,1 with 1 ≤ p 〈 ＋∞. Our result relies on a new a priori estimate for the velocity, where we introduce a new unknown called effective velocity to weaken one of the couplings between the density and the velocity. In particular, our result is the first in which we obtain uniqueness without imposing hypothesis on the gradient of the density.
文摘In this paper, we study the dynamics of a diffusive modified Leslie-Cower model with the multiplicative Allee effect and Ba^zykin functional response. We give detailed study on the stability of equilibria. Non-existence of non-constant positive steady state solutions are shown to identify the rage of parameters of spatial pattern formation. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns.
