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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...
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...
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....
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 ...
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...
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 ...
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...
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     Hylomorphic  solitons  dynamics       font style='font-size:12px;'> 2015/4/3
Hylomorphic solitons and their dynamics.
Consider a branch of unstable solitons of NLS whose linearized operators have one pair of simple real eigenvalues in addition to the zero eigenvalue. Under radial symmetry and standard assumptions, so...
Solitons confined in channels are studied in the two-dimensional nonlinear Schr\"odinger equation. We study the dynamics of two channel-guided solitons near the junction where two channels are merged....
The H-flow translating solitons in R^3 and R^4     H-flow translating solitons  R^3  R^4  Differential Geometry       font style='font-size:12px;'> 2012/4/17
Motivated by Ilmanen's correspondence, we present an explicit solution to the prescribed Hoffman-Osserman Gauss map problem for non-minimal translators to the mean curvature flow in Euclidean 4-space....
Abstract: In this paper we describe the inelastic character of solitons of some slowly varying gKdV equations. We give precise lower bounds, in the energy space, of the defect induced by the potential...
Bach-flat gradient steady Ricci solitons     Bach-flat gradient  Ricci solitons  Differential Geometry       font style='font-size:12px;'> 2011/9/19
Abstract: In this paper we prove that any $n$-dimensional ($n\ge 4$) complete Bach-flat gradient steady Ricci solitons with positive Ricci curvature is isometric to the Bryant soliton. We also show th...
Abstract: We will give a simple proof that the metric of any compact Yamabe gradient soliton (M,g) is a metric of constant scalar curvature when the dimension of the manifold n>2.

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