arXiv subjects

Zechuan Zhang

Publications and source records attributed to Zechuan Zhang.

15 recordsLinked to original sources

arXiv2026

Inverse scattering for the focusing nonlinear Schr\"odinger equation with elliptic background and full soliton gas

In this manuscript we develop the direct and inverse scattering problem for the cubic focusing nonlinear Schr\"odinger equation and for initial data that are asymptotic to an elliptic travelling wave with distinct phase at $\pm \infty$. We consider the case in which the spectral bands intersect the real axis. We then show that this class of initial data has non zero intersection with the full soliton gas initial data.

math.AP↗

arXiv2026

TRACE: High-Fidelity 3D Scene Editing via Tangible Reconstruction and Geometry-Aligned Contextual Video Masking

Existing 3D Gaussian Splatting (3DGS) editing methods primarily focus on appearance modification and often struggle to support flexible geometry editing while preserving structural integrity and scene-consistent appearance. To address this limitation, we present TRACE, a mesh-guided 3DGS editing framework that automatically aligns explicit 3D geometry with Gaussian scenes and decouples Geometric Anchoring from Appearance Harmonization. First, Multi-view 3D-Anchor Synthesis, trained on our MV-TRACE dataset for scene-coherent object addition and modification, generates geometrically aligned editing anchors, while Tangible Geometry Alignment (TGA) performs coarse-to-fine mesh-scene registration. Then, Contextual Video Masking (CVM) integrates projected 3D anchors into an autoregressive video diffusion pipeline, harmonizing their appearance with the surrounding scene while maintaining multi-view consistency. We evaluate TRACE on eight held-out scenes across six editing categories. TRACE completes each edit in approximately 10 minutes on a single NVIDIA RTX Pro 6000 GPU. Extensive experiments demonstrate consistent improvements over existing methods in editing versatility, structural integrity, semantic alignment, multi-view consistency, and visual quality.

cs.CV↗

arXiv2026

Direct Scattering of the Focusing Nonlinear Schr\"odinger Equation with Step-like Oscillatory Initial Data

In this manuscript we set up the direct and inverse scattering problems for step-like traveling-wave solutions of the nonlinear Schr\"odinger equation. Specifically, we consider initial data $u(x,0)$ satisfying $u(x,0)\to u_0^\ell(x)$ as $x\to-\infty$ and $u(x,0)\to u_0^r(x)$ as $x\to+\infty$, where $u_0^\ell(x)$ and $u_0^r(x)$ are elliptic traveling waves. Under suitable assumptions on the initial data we formulate the direct scattering problem and establish analytic properties of the scattering data. We then formulate the inverse problem as a Riemann--Hilbert problem and prove its solvability. Finally, we observe that this Riemann--Hilbert formulation is a special case of the one arising for full soliton-gas initial data.

math.AP↗

arXiv2025

Semiclassical dynamics and coherent soliton ensembles in the derivative nonlinear Schr\"odinger equation with periodic initial conditions

The semiclassical limit of the derivative nonlinear Schrodinger equation with periodic initial conditions is studied analytically and numerically. The spectrum of the associated scattering problem for a certain class of initial conditions, referred to as periodic single-lobe potentials, is numerically computed, and it is shown that the spectrum becomes confined to the real and imaginary axes or the spectral parameter in the semiclassical limit. A formal Wentzel-Kramers-Brillouin expansion is computed for the scattering eigenfunctions, which allows one to obtain asymptotic expressions for the number, location and size of the spectral bands and gaps. The results of these calculations suggest that, in the semiclassical limit, all excitations in the spectrum become effective solitons. Finally, the analytical predictions are compared with direct numerical simulations as well as with numerical calculations of the Lax spectrum, and the results are shown to be in excellent agreement.

nlin.SI↗

arXiv2025

Are Image-to-Video Models Good Zero-Shot Image Editors?

Large-scale video diffusion models show strong world simulation and temporal reasoning abilities, but their use as zero-shot image editors remains underexplored. We introduce IF-Edit, a tuning-free framework that repurposes pretrained image-to-video diffusion models for instruction-driven image editing. IF-Edit addresses three key challenges: prompt misalignment, redundant temporal latents, and blurry late-stage frames. It includes (1) a chain-of-thought prompt enhancement module that transforms static editing instructions into temporally grounded reasoning prompts; (2) a temporal latent dropout strategy that compresses frame latents after the expert-switch point, accelerating denoising while preserving semantic and temporal coherence; and (3) a self-consistent post-refinement step that sharpens late-stage frames using a short still-video trajectory. Experiments on four public benchmarks, covering non-rigid editing, physical and temporal reasoning, and general instruction edits, show that IF-Edit performs strongly on reasoning-centric tasks while remaining competitive on general-purpose edits. Our study provides a systematic view of video diffusion models as image editors and highlights a simple recipe for unified video-image generative reasoning.

cs.CV↗

arXiv2025

Spectral theory for non-self-adjoint Dirac operators with periodic potentials and inverse scattering transform for the focusing nonlinear Schr\"odinger equation with periodic boundary conditions

We formulate the inverse spectral theory for a non-self-adjoint one-dimensional Dirac operator associated periodic potentials via a Riemann-Hilbert problem approach. We use the resulting formalism to solve the initial value problem for the focusing nonlinear Schr\"odinger equation. We establish a uniqueness theorem for the solutions of the Riemann-Hilbert problem, which provides a new method for obtaining the potential from the spectral data. The formalism applies for both finite- and infinite-genus potentials. As in the defocusing case, the formalism shows that only a single set of Dirichlet eigenvalues is needed in order to uniquely reconstruct the potential of the Dirac operator and the corresponding solution of the focusing NLS equation.

nlin.SI↗

arXiv2025

In-Context Edit: Enabling Instructional Image Editing with In-Context Generation in Large Scale Diffusion Transformer

Instruction-based image editing enables precise modifications via natural language prompts, but existing methods face a precision-efficiency tradeoff: fine-tuning demands massive datasets (>10M) and computational resources, while training-free approaches suffer from weak instruction comprehension. We address this by proposing ICEdit, which leverages the inherent comprehension and generation abilities of large-scale Diffusion Transformers (DiTs) through three key innovations: (1) An in-context editing paradigm without architectural modifications; (2) Minimal parameter-efficient fine-tuning for quality improvement; (3) Early Filter Inference-Time Scaling, which uses VLMs to select high-quality noise samples for efficiency. Experiments show that ICEdit achieves state-of-the-art editing performance with only 0.1\% of the training data and 1\% trainable parameters compared to previous methods. Our approach establishes a new paradigm for balancing precision and efficiency in instructional image editing. Codes and demos can be found in https://river-zhang.github.io/ICEdit-gh-pages/.

cs.CV↗

arXiv2025

3D Object Manipulation in a Single Image using Generative Models

Object manipulation in images aims to not only edit the object's presentation but also gift objects with motion. Previous methods encountered challenges in concurrently handling static editing and dynamic generation, while also struggling to achieve fidelity in object appearance and scene lighting. In this work, we introduce \textbf{OMG3D}, a novel framework that integrates the precise geometric control with the generative power of diffusion models, thus achieving significant enhancements in visual performance. Our framework first converts 2D objects into 3D, enabling user-directed modifications and lifelike motions at the geometric level. To address texture realism, we propose CustomRefiner, a texture refinement module that pre-train a customized diffusion model, aligning the details and style of coarse renderings of 3D rough model with the original image, further refine the texture. Additionally, we introduce IllumiCombiner, a lighting processing module that estimates and corrects background lighting to match human visual perception, resulting in more realistic shadow effects. Extensive experiments demonstrate the outstanding visual performance of our approach in both static and dynamic scenarios. Remarkably, all these steps can be done using one NVIDIA 3090. Project page is at https://whalesong-zrs.github.io/OMG3D-projectpage/

cs.CV↗

arXiv2024

Local and global well-posedness of the Maxwell-Bloch system of equations with inhomogeneous broadening

The Maxwell-Bloch system of equations with inhomogeneous broadening is studied, and the local and global well-posedness of the corresponding initial-boundary value problem is established by taking advantage of the integrability of the system and making use of the corresponding inverse scattering transform. A key ingredient in the analysis is the $L^2$-Sobolev bijectivity of the direct and inverse scattering transform established by Xin Zhou for the focusing Zakharov-Shabat problem.

nlin.SI↗

arXiv2024

Rethinking the Architecture Design for Efficient Generic Event Boundary Detection

Generic event boundary detection (GEBD), inspired by human visual cognitive behaviors of consistently segmenting videos into meaningful temporal chunks, finds utility in various applications such as video editing and. In this paper, we demonstrate that SOTA GEBD models often prioritize final performance over model complexity, resulting in low inference speed and hindering efficient deployment in real-world scenarios. We contribute to addressing this challenge by experimentally reexamining the architecture of GEBD models and uncovering several surprising findings. Firstly, we reveal that a concise GEBD baseline model already achieves promising performance without any sophisticated design. Secondly, we find that the widely applied image-domain backbones in GEBD models can contain plenty of architecture redundancy, motivating us to gradually ``modernize'' each component to enhance efficiency. Thirdly, we show that the GEBD models using image-domain backbones conducting the spatiotemporal learning in a spatial-then-temporal greedy manner can suffer from a distraction issue, which might be the inefficient villain for GEBD. Using a video-domain backbone to jointly conduct spatiotemporal modeling is an effective solution for this issue. The outcome of our exploration is a family of GEBD models, named EfficientGEBD, significantly outperforms the previous SOTA methods by up to 1.7\% performance gain and 280\% speedup under the same backbone. Our research prompts the community to design modern GEBD methods with the consideration of model complexity, particularly in resource-aware applications. The code is available at \url{https://github.com/Ziwei-Zheng/EfficientGEBD}.

cs.CV↗

arXiv2024

SIFU: Side-view Conditioned Implicit Function for Real-world Usable Clothed Human Reconstruction

Creating high-quality 3D models of clothed humans from single images for real-world applications is crucial. Despite recent advancements, accurately reconstructing humans in complex poses or with loose clothing from in-the-wild images, along with predicting textures for unseen areas, remains a significant challenge. A key limitation of previous methods is their insufficient prior guidance in transitioning from 2D to 3D and in texture prediction. In response, we introduce SIFU (Side-view Conditioned Implicit Function for Real-world Usable Clothed Human Reconstruction), a novel approach combining a Side-view Decoupling Transformer with a 3D Consistent Texture Refinement pipeline.SIFU employs a cross-attention mechanism within the transformer, using SMPL-X normals as queries to effectively decouple side-view features in the process of mapping 2D features to 3D. This method not only improves the precision of the 3D models but also their robustness, especially when SMPL-X estimates are not perfect. Our texture refinement process leverages text-to-image diffusion-based prior to generate realistic and consistent textures for invisible views. Through extensive experiments, SIFU surpasses SOTA methods in both geometry and texture reconstruction, showcasing enhanced robustness in complex scenarios and achieving an unprecedented Chamfer and P2S measurement. Our approach extends to practical applications such as 3D printing and scene building, demonstrating its broad utility in real-world scenarios. Project page https://river-zhang.github.io/SIFU-projectpage/ .

cs.CV↗

arXiv2023

Spectral theory for self-adjoint Dirac operators with periodic potentials and inverse scattering transform for the defocusing nonlinear Schroedinger equation with periodic boundary conditions

The inverse spectral theory for a self-adjoint one-dimensional Dirac operator associated periodic potentials is formulated via a Riemann-Hilbert problem approach. The resulting formalism is also used to solve the initial value problem for the nonlinear Schrodinger (NLS) equation. A uniqueness theorem for the solutions of the Riemann-Hilbert problem is established, which provides a new method for obtaining the potential from the spectral data. Two additional, scalar Riemann-Hilbert problems are also formulated that provide conditions for the periodicity in space and time of the solution generated by arbitrary sets of spectral data. The formalism applies for both finite-genus and infinite-genus potentials. The formalism also shows that only a single set of Dirichlet eigenvalues is needed in order to uniquely reconstruct the potential of the Dirac operator and the corresponding solution of the defocusing NLS equation, in contrast with the representation of the solution of the NLS equation via the finite-genus formalism, in which two different sets of Dirichlet eigenvalues are used.

math.AP↗

arXiv2023

Global-correlated 3D-decoupling Transformer for Clothed Avatar Reconstruction

Reconstructing 3D clothed human avatars from single images is a challenging task, especially when encountering complex poses and loose clothing. Current methods exhibit limitations in performance, largely attributable to their dependence on insufficient 2D image features and inconsistent query methods. Owing to this, we present the Global-correlated 3D-decoupling Transformer for clothed Avatar reconstruction (GTA), a novel transformer-based architecture that reconstructs clothed human avatars from monocular images. Our approach leverages transformer architectures by utilizing a Vision Transformer model as an encoder for capturing global-correlated image features. Subsequently, our innovative 3D-decoupling decoder employs cross-attention to decouple tri-plane features, using learnable embeddings as queries for cross-plane generation. To effectively enhance feature fusion with the tri-plane 3D feature and human body prior, we propose a hybrid prior fusion strategy combining spatial and prior-enhanced queries, leveraging the benefits of spatial localization and human body prior knowledge. Comprehensive experiments on CAPE and THuman2.0 datasets illustrate that our method outperforms state-of-the-art approaches in both geometry and texture reconstruction, exhibiting high robustness to challenging poses and loose clothing, and producing higher-resolution textures. Codes will be available at https://github.com/River-Zhang/GTA.

cs.CV↗

arXiv2023

On the Cauchy problem of defocusing mKdV equation with finite density initial data: long time asymptotics in soliton-less regions

We investigate the long-time asymptotics for the solutions to the Cauchy problem of defocusing modified Kortweg-de Vries (mKdV) equation with finite density initial data. The present paper is the subsequent work of our previous paper [arXiv:2108.03650], which gives the soliton resolution for the defocusing mKdV equation in the central asymptotic sector $\{(x,t): \vert ξ\vert<6\}$ with $ξ:=x/t$. In the present paper, via the Riemann-Hilbert (RH) problem associated to the Cauchy problem, the long-time asymptotics in the soliton-less regions $\{(x,t): \vert ξ\vert>6, |ξ|=\mathcal{O}(1)\}$ for the defocusing mKdV equation are further obtained. It is shown that the leading term of the asymptotics are in compatible with the ``background solution'' and the error terms are derived via rigorous analysis.

math.AP↗

arXiv2021

Soliton resolution and asymptotic stability of $N$-soliton solutions for the defocusing mKdV equation with a non-vanishing background

We analytically study the large-time asymptotics of the solution of the defocusing modified Korteweg-de Vries (mKdV) equation under a symmetric non-vanishing background, which supports the emergence of solitons. It is demonstrated that the asymptotic expansion of the solution at the large time could verify the renowned soliton resolution conjecture. Moreover, the asymptotic stability of $N$-soliton solution is also exhibited in the present work. We establish our results by performing a $\bar{\partial}$-nonlinear steepest descent analysis to the associated Riemann-Hilbert (RH) problem.

math.AP↗