10 papers
Domain dependence of Sobolev-curl constants and structure of critical curl-curl solutions
Yong Liu, Jun Wang, Xuan Wang +1
This paper investigates intrinsic critical Sobolev-curl constants on bounded domains and the structure of finite-energy solutions to the critical curl-curl equation in R^3. First,…
On Brezis' open problem 2.2
Hong-Ge Chen, Yong Liu, Juncheng Wei +1
We prove that the global minimizer of the Ginzburg-Landau energy in the disk of radius with boundary value is the degree-one radial solution of the planar…
Nonradial stable solutions near the Joseph--Lundgren threshold
Shibing Chen, Yong Liu, Juncheng Wei +1
We study positive stable solutions of the supercritical Lane--Emden equation in the first Joseph--Lundgren interval. For a family of dimensions, we construct nonradial stable entir…
Nondegeneracy and Morse Index of Ginzburg--Landau Vortices
Manuel del Pino, Yong Liu, Monica Musso +2
We prove that the standard degree-two and degree-three vortex solutions of the Ginzburg-Landau equation are nondegenerate. Their Morse indices are also computed. The proof relies o…
On Sirakov's equal-frequency uniqueness conjecture
Hong-Ge Chen, Yong Liu, Juncheng Wei +1
Let , , and . We prove that the equal-frequency two-component cubic Schrödinger system \[ -Δu+u=μ_1u^3+βuv^2, \qquad -Δv+v=μ_2v^3+βu^2v \quad\te…
Symmetry breaking for the complex sine-Gordon equation
Shibing Chen, Changfeng Gui, Yong Liu +2
We consider the existence of vortex solutions to the complex sine-Gordon II (CSG2) equation, which can be viewed as an analogy of the Ginzburg-Landau (GL) equation. Using the nontr…
Stability of Solitary Capillary-Gravity Water Waves in Three Dimensions
Changfeng Gui, Shanfa Lai, Yong Liu +2
This paper establishes the conditional orbital stability of fully localized solitary waves for the three-dimensional capillary-gravity water wave problem in finite depth under stro…
From KP-I Lump Solution to Travelling wave of 3D Gravity Capillary Water wave problem
Changfeng Gui, Shanfa Lai, Yong Liu +2
In this paper, we study the three-dimensional gravity-capillary water wave problem involving an irrotational, perfect fluid with gravity and surface tension. We focus on steady wav…
Toda lattice and Riemann type minimal surfaces
Changfeng Gui, Yong Liu, Jun Wang +1
Toda lattice and minimal surfaces are related to each other through Allen-Cahn equation. In view of the structure of the solutions of the Toda lattice, we find new balancing config…
Lump type solutions: Backlund transformation and spectral properties
Yong Liu, Jun-cheng Wei, Wen Yang
There are various different ways to obtain traveling waves of lump type for the KP equation. We propose a general and simple approach to derive them via a Backlund transformation.…