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Jifeng Chu

Publications and source records attributed to Jifeng Chu.

9 recordsLinked to original sources
arXiv2026

Large-Amplitude Steady Solitary Water Waves with General Vorticity

We study two-dimensional steady solitary gravity water waves with general vorticity, allowing for overhanging free-surface profiles. The main challenges arise from the free boundary, the unbounded fluid domain, and the inherent complexity of the general vorticity setting. To address these, we introduce a conformal reformulation that reduces the problem to an equivalent system on a fixed strip, consisting of an overdetermined elliptic problem coupled with an elliptic boundary-value problem. This framework enables a local analysis without imposing restrictive assumptions on the vorticity. Using the center-manifold construction of Chen, Walsh and Wheeler \cite{chennonlinearity}, we first establish the existence of small-amplitude solitary waves for such non-trivial vorticity distributions. Subsequently, via a global analytic bifurcation argument, we prove the existence of continuous branches of large-amplitude solitary waves for analytic vorticity functions. Along these global solution curves, the free surfaces may develop overhanging profiles and need not remain graphs over the horizontal coordinate. Our results provide a new constructive framework for large-amplitude solitary waves with general vorticity, extending the existing theory beyond the classical settings of constant vorticity \cite{susannaarma} and non-overhanging profiles \cite{milesjma}.

math.AP↗
arXiv2026

Global bifurcation of water-wave fronts generated by surface pressure

We study two-dimensional steady gravity water waves with general vorticity in a homogeneous, inviscid fluid of finite depth, subject to a surface pressure that tends to distinct constants upstream and downstream. Starting from a fixed supercritical shear flow, we construct two global branches of monotone fronts connecting distinct laminar states, with increasing and decreasing profiles corresponding to the two signs of the pressure transition. Small-amplitude fronts are first obtained via the implicit function theorem and then extended by analytic global continuation.

math.AP↗
arXiv2026

Optimal bounds for embedded eigenvalues of one-dimensional discrete Schrödinger operators with decaying potentials

In this paper, we consider one-dimensional discrete Schrödinger operators \begin{align} Hu(n)=(Δ+V)u(n)\nonumber \end{align} on $\ell^2(\mathbb{N})$ with a self-adjoint boundary condition at $n=0$, where $Δ$ denotes the discrete Laplacian and $V(n)$ is a real-valued perturbation satisfying $$V(n)=\frac{O(1)}{1+n}.$$ We determine the sharp transition for the asymptotic coefficient of \(V\) governing the existence and nonexistence of embedded eigenvalues.

math-ph↗
arXiv2025

Explicit sharp bounds for all nodes of Sturm-Liouville operators with potentials in $L^1$ balls

For the classical Sturm-Liouville operators, we prove the sharp bounds for all nodes of eigenfunctions by regarding these nodes as nonlinear functionals of potential $q\in L^1[0,1]$. By studying the optimization problems to minimize or to maximize the nodes $\{ T_{i,m}\}$ subject to the constraint $\|q\|_{1}=r$ with $r>0$ and using the strong continuity of the nodes in potentials, we obtain the explicit expressions for the sharp bounds, which are given as elementary functions.

math.SP↗
arXiv2025

Weak separability and partial Fermi isospectrality of discrete periodic Schrödinger operators

In this paper, we consider the discrete periodic Schrödinger operators $Δ+V$ on $\Z^d$, where $V$ is $Γ$-periodic with $Γ=q_1 \mathbb{Z}\oplus q_2\mathbb{Z}\oplus\cdots\oplus q_d\mathbb{Z}$ and positive integers $q_j$, $j=1,2,\cdots,d,$ are pairwise coprime. We introduce the notions of generalized partial Fermi isospectrality and weak separability, and prove that two generalized partially Fermi isospectral potentials have the same weak separability. As a direct application, we can prove that two potentials have the same $(d_1,d_2,\cdots,d_r)$-separability by assuming that they are generalized partially Fermi isospectral, instead of the Fermi isospectrality or Floquet isospectrality. Besides, we prove that each couples of components of the generalized Fermi isospectral potentials are Floquet isospectral in some sense.

math.SP↗
arXiv2019

Constant vorticity geophysical waves with centripetal forces and at arbitrary latitude

We consider three-dimensional geophysical flows at arbitrary latitude and with constant vorticity beneath a wave train and above a flat bed in the $β$-plane approximation with centripetal forces. We consider the $f$-plane approximation as well as the $β$-plane approximation. For the $f$-plane approximation, we prove that there is no bounded solution. For the $β$-plane approximation, we show that the flow is necessarily irrotational and the free surface is necessarily flat if it exhibits a constant vorticity. Our results reveal some essential differences from those results in the literature, due to the presence of centripetal forces. Moreover, for the case exhibiting the surface tension, we prove that there are no flows exhibiting constant vorticity.

math.AP↗
arXiv2007

Existence of positive solutions for nonlinear systems

This paper deals with the existence of positive solutions for the nonlinear system q(t)ϕ(p(t)u'_{i}(t)))'+f^{i}(t,\textbf{u})=0,\quad 0<t<1,\quad i=1,2,...,n. This system often arises in the study of positive radial solutions of nonlinear elliptic system. Here $\textbf{u}=(u_{1},...,u_{n})$ and $f^{i}, i=1,2,...,n$ are continuous and nonnegative functions, $p(t), q(t)\hbox{\rm :} [0,1]\to (0,\oo)$ are continuous functions. Moreover, we characterize the eigenvalue intervals for (q(t)ϕ(p(t)u'_{i}(t)))'+λh_{i}(t)g^{i} (\textbf{u})=0, \quad 0<t<1,\quad i=1,2,...,n. The proof is based on a well-known fixed point theorem in cones.

math.AP↗