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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Liouville Properties on gradient shrinking Ricci solitons with constant scalar curvature
常标量 曲率梯度收缩 Ricci孤子 Liouville性质
2023/11/13
In this talk we show that bounded harmonic functions are constant on gradient shrinking Ricci solitons with CSC by frequency function method. As an application, we show that the space of harmonic func...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Solitons and Breathers in the modulus KdV equations
模量 KdV方程 孤子 呼吸器
2023/5/12
Compared to the soliton solutions, the breathers, which are constructed in the mKdV or Gardner equation via integrability methods, are less studied. In our numerical study, we show the interactions be...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On forward/inverse spectral problems, approximation problems and multiple integral formulae for non-smooth solitons
非光滑孤子 正/逆谱问题 近似问题 多重积分公式
2023/4/28
A class of nonlinear integrable PDEs admit non-smooth solitary wave solutions as certain special weak solutions. These solutions can be used to capture main attributes of solutions of these PDEs, e.g....
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Dynamics of multi-solitons to Klein-Gordon equations
多孤子 克莱因-戈登方程 动力学
2023/4/21
I will report my recent joint work with Jacek Jendrej on muti-solitons to the Klein-Gordon equations including their asymptotic stability and classification.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：O(2)-symmetry of 3D steady gradient solitons
O(2) 三维稳态 梯度孤子 对称性
2023/4/13
In this talk, we talk about the proof of the O(2)-symmetry of 3D steady gradient solitons. The proof consists of four parts: the asymptotic analysis at infinity, the symmetry improvement theorem, the ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent results on multi-bubble blow-ups and multi-solitons to stochastic nonlinear Schroinger equations
多气泡膨胀 多孤子 随机非线性 Schroinger equations
2023/4/13
In this talk we review some recent results on the multi-bubble blow-ups and multi-solitons to the focusing stochastic nonlinear Schr鰀inger equations. We will show the corresponding construction and co...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Recent results on multi-bubble blow-ups and multi-solitons to stochastic nonlinear Schroinger equations
多气泡膨胀 多孤子 随机非线性 薛定谔方程
2023/4/18
In this talk we review some recent results on the multi-bubble blow-ups and multi-solitons to the focusing stochastic nonlinear Schr鰀inger equations. We will show the corresponding construction and co...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Construction of steady gradient solitons by interpolation
插值 稳态梯度孤子 坍塌式
2023/4/13
In this talk, we give an overall description of the construction of the collapsed flying-wing-like steady gradient solitons, as well as the high dimension non-collapsed steady gradient solitons. In pa...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Steady gradient Ricci solitons with positive curvature
正曲率 稳态梯度 利玛窦孤子
2023/4/17
We will construct some new examples of steady gradient Ricci solitons with positive curvature operator. Moreover, for any 3D steady gradient Ricci soliton with positive curvature, if it is asymptotic ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A Survey of Stability of Peaked Solitons II: Multicomponent Case
峰值孤子 稳定性 多组分案例
2023/4/27
Peaked soliton dynamics is one of the most intriguing features of the Camassa-Holm-type integrable equations. In this talk, I will give a review on the issue of the stability of peaked solitons, inclu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A Survey of Stability of Peaked Solitons I: Scalar Case
峰值孤子 稳定性 标量案例
2023/4/27
Peaked soliton dynamics is one of the most intriguing features of the Camassa-Holm-type integrable equations. In this talk, I will give a review on the issue of the stability of peaked solitons, inclu...
ON LOCALLY CONFORMALLY FLAT GRADIENT SHRINKING RICCI SOLITONS
SHRINKING RICCI SOLITONS CONFORMALLY FLAT
2015/8/17
In this paper, we first apply an integral identity on Ricci solitons to prove that
closed locally conformally flat gradient Ricci solitons are of constant sectional curvature.
We then ge...
Compact Gradient Shrinking Ricci Solitons with Positive Curvature Operator
Positive Curvature Operator Shrinking Ricci Solitons
2015/8/17
In this paper, we first derive several identities on a compact shrinking Ricci
soliton. We then show that a compact gradient shrinking soliton must be
Einstein, if it admits a Riemannian metri...
Hylomorphic solitons and their dynamics.
Solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity
Stability in two-dimensional discrete nonlinear schrodinger equation lattice discrete soliton
2014/12/29
We study the existence and stability of localized states in the discrete nonlinear Schrödinger equation on two-dimensional nonsquare lattices. The model includes both the nearest-neighbor and lon...