The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutio...The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions （including kinky periodic solitary-wave solutions, periodic soliton solutions, and cross kink-wave solutions） for the new （2＋1）-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensionai nonlinear wave field.展开更多
We investigate the multiplicity of positive steady state solutions to the unstirred chemostat model with general response functions. It turns out that all positive steady state solutions to this model lie on a single ...We investigate the multiplicity of positive steady state solutions to the unstirred chemostat model with general response functions. It turns out that all positive steady state solutions to this model lie on a single smooth solution curve, whose properties determine the multiplicity of positive steady state solutions. The key point of our analysis is to study the ＂turning points＂ on this positive steady state solution curve, and to prove that any nontrivial solution to the associated linearized problem is one of sign by constructing a suitable test function. The main tools used here include bifurcation theory, monotone method, mountain passing lemma and Sturm comnarison theorem.展开更多
Model ChemLab是美国Model Science公司研制的一款交互式化学实验模拟软件。它能形象地显示化学实验仪器,提供预先设置好的化学实验,还能根据使用者的需要,借助实验室向导工具的帮助,很容易地创造出新的模拟实验,是目前化学实验教学最...Model ChemLab是美国Model Science公司研制的一款交互式化学实验模拟软件。它能形象地显示化学实验仪器,提供预先设置好的化学实验,还能根据使用者的需要,借助实验室向导工具的帮助,很容易地创造出新的模拟实验,是目前化学实验教学最好的计算机辅助教学软件之一。一、Model展开更多
基金Supported by the Natural Science Foundation of China under Grant Nos.10361007,10661002Yunnan Natural Science Foundation under Grant No.2006A0082M
文摘The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions （including kinky periodic solitary-wave solutions, periodic soliton solutions, and cross kink-wave solutions） for the new （2＋1）-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensionai nonlinear wave field.
基金supported by National Natural Science Foundation of China(Grant Nos.11001160 and 11271236)Natural Science Foundation of Shaanxi Province(Grant No.2011JQ1015)the Fundamental Research Funds for the Central Universities(Grant Nos.GK201001002 and GK201002046)
文摘We investigate the multiplicity of positive steady state solutions to the unstirred chemostat model with general response functions. It turns out that all positive steady state solutions to this model lie on a single smooth solution curve, whose properties determine the multiplicity of positive steady state solutions. The key point of our analysis is to study the ＂turning points＂ on this positive steady state solution curve, and to prove that any nontrivial solution to the associated linearized problem is one of sign by constructing a suitable test function. The main tools used here include bifurcation theory, monotone method, mountain passing lemma and Sturm comnarison theorem.
