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Article
Open AccessCoexistence of superconductivity and topological phase in kagome metals ANb3Bi5 (A = K, Rb, Cs)
The AV3Sb5 prototype kagome materials have been demonstrated as a versatile platform for exploring exotic properties in condensed matter physics, including charge density waves, superconductivity, non-trivial ele...
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Article
Open AccessInducing and tuning Kondo screening in a narrow-electronic-band system
Although the single-impurity Kondo physics has already been well understood, the understanding of the Kondo lattice where a dense array of local moments couples to the conduction electrons is still far from co...
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Article
Open AccessStructural phase transition and superconductivity hierarchy in 1T-TaS2 under pressure up to 100 GPa
The adoption of high pressure not only reinforces the comprehension of the structure and exotic electronic states of transition metal dichalcogenides (TMDs) but also promotes the discovery of intriguing phenom...
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Whiskered Tori for Forced Beam Equations with Multi-dimensional Liouvillean Frequency
In this paper we develop a Kolmogorov–Arnold–Moser (KAM) theory close to two fixed points for quasi-periodically forced nonlinear beam equation $$\begin{aligned} \begin{aligned} y_{tt}+my+y_{xxxx}=y^{3}+ \varepsi...
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Article
Response Solution to Ill-Posed Boussinesq Equation with Quasi-Periodic Forcing of Liouvillean Frequency
In this paper, we prove the existence of response solution (i.e., quasi-periodic solution with the same frequency as the forcing) for the quasi-periodically forced generalized ill-posed Boussinesq equation: $$\be...
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Article
Periodic and Quasi-Periodic Solutions for Reversible Unbounded Perturbations of Linear Schrödinger Equations
In this paper, we consider a new class of derivative nonlinear Schrödinger equations with reversible nonlinearities of the form $$\begin{aligned} \mathrm {i}u_t+u_{xx}+|u_x|^{4}u=0,\quad (t, x)\in {\mathbb {R}}\t...
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Article
Quasi-Periodic Solutions for the Reversible Derivative Nonlinear Schrödinger Equations with Periodic Boundary Conditions
In this paper, we prove the existence of small amplitude, smooth time quasi-periodic solutions for a class of reversible derivative nonlinear Schrödinger equations with periodic boundary conditions. The proof ...
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Article
Invariant tori for reversible nonlinear Schrödinger equations under quasi-periodic forcing
In this paper, by infinite-dimensional reversible KAM (Kolmogorov–Arnold–Moser) theory, we prove the existence of invariant tori (thus quasi-periodic solutions) for a class of quasi-periodically forced reversi...
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Article
Open AccessAn anisotropic quasilinear problem with perturbations
This work focuses on proving the existence and uniqueness of strong solutions of perturbed anisotropic total variation flow with the Neumann boundary condition when the initial data is an
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A result on quasi-periodic solutions of a nonlinear beam equation with a quasi-periodic forcing term
In this paper, a quasi-periodically forced nonlinear beam equation \({u_{tt}+u_{xxxx}+\mu u+\varepsilon\phi(t)h(u)=0}\) ...
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Article
Small Divisor Problem in Dynamical Systems and Analytic Solutions of a q-Difference Equation with a Singularity at the Origin
In this paper, we consider a q-difference equation $$\sum_{j=0}^{k}\sum_{t=1}^{\infty}C_{t,j}(z)(y(q^jz))^{t}=G(z)$$ i...
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Article
Construction of convex solutions for the second type of Feigenbaum’s functional equations
In this paper, convex solutions for the second type of Feigenbaum’s equation $$ \left\{ \begin{gathered} f(x) = \frac{1} {\lambda }f...
