Results 61 to 70 of about 217,226 (371)

Dressing method based on homogeneous Fredholm equation: quasilinear PDEs in multidimensions

, 2007
In this paper we develop a dressing method for constructing and solving some classes of matrix quasi-linear Partial Differential Equations (PDEs) in arbitrary dimensions.
A I Zenchuk, Ablowitz M J, Bogdanov L V, Bruschi M, Calogero F, Konopelchenko B, Korteweg D J, P M Santini, Santini P M Zenchuk A I, Tsarev S P, Whitham J B, Zakharov V E, Zakharov V E, Zakharov V E, Zakharov V E, Zakharov V E, Zakharov V E, Zenchuk A, Zenchuk A I, Zenchuk A I, Zenchuk A I   +20 more
core   +3 more sources

Asymptotic analysis of the biharmonic Schrödinger equation with fractional damping

Boundary Value Problems
In this paper, we study the decay behavior of solutions to the biharmonic Schrödinger equation under the effect of internal fractional damping. By employing semigroup theory and energy methods, we establish well-posedness results and investigate the long-
Khadidja Fekirini, Naima Louhibi, Ibrahim Meradjah, Salah Boulaaras, Mohamed Hocine Braiki   +4 more
doaj   +1 more source

The Inverse Spectral Transform for the Dunajski hierarchy and some of its reductions, I: Cauchy problem and longtime behavior of solutions

, 2015
In this paper we apply the formal Inverse Spectral Transform for integrable dispersionless PDEs arising from the commutation condition of pairs of one-parameter families of vector fields, recently developed by S. V. Manakov and one of the authors, to one
Santini, P. M., Yi, G.
core   +1 more source

Topology and Material Optimization in Ultra‐Soft Magneto‐Active Structures: Making Advantage of Residual Anisotropies

Advanced Materials, EarlyView.
Residual magnetization induces pronounced mechanical anisotropy in ultra‐soft magnetorheological elastomers, shaping deformation and actuation even without external magnetic fields. This study introduces a computational‐experimental framework integrating magneto‐mechanical coupling into topology optimization for designing soft magnetic actuators with ...
Carlos Perez‐Garcia, Rogelio Ortigosa, Jesús Martínez‐Frutos, Daniel Garcia‐Gonzalez   +3 more
wiley   +1 more source

Portopulmonary hypertension practice patterns after liver transplantation

Liver Transplantation, EarlyView., 2022
Abstract Portopulmonary hypertension (POPH) is a type of pulmonary arterial hypertension occurring exclusively in those with portal hypertensive liver disease. Liver transplantation (LT) can significantly improve outcomes. Current guidelines counsel against immediate adjustments to targeted therapy after LT and suggest routine echocardiography as ...
Arun Jose, Elizabeth J. Kopras, Shimul A. Shah, Jean M. Elwing   +3 more
wiley   +1 more source

Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs [PDF]

Journal of Computational Physics, 2019
This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional construction and ...
Z. Cai, Jingshuang Chen, Min Liu, Xinyu Liu   +3 more
semanticscholar   +1 more source

AutomataGPT: Transformer‐Based Forecasting and Ruleset Inference for Two‐Dimensional Cellular Automata

Advanced Science, EarlyView.
We introduce AutomataGPT, a generative pretrained transformer (GPT) trained on synthetic spatiotemporal data from 2D cellular automata to learn symbolic rules. Demonstrating strong performance on both forward and inverse tasks, AutomataGPT establishes a scalable, domain‐agnostic framework for interpretable modeling, paving the way for future ...
Jaime A. Berkovich, Noah S. David, Markus J. Buehler   +2 more
wiley   +1 more source

On the relationship between nonlinear equations integrable by the method of characteristics and equations associated with commuting vector fields

, 2009
It was shown recently that Frobenius reduction of the matrix fields reveals interesting relations among the nonlinear Partial Differential Equations (PDEs) integrable by the Inverse Spectral Transform Method ($S$-integrable PDEs), linearizable by the ...
A. I. Zenchuk, Kadomtsev B. B., Manakov S. V., Whitham J. B., Zakharov V. E., Zakharov V. E., Zakharov V. E.   +6 more
core   +1 more source

PDE-PRESERVING PROPERTIES [PDF]

Journal of the Korean Mathematical Society, 2005
A continuous linear operator \(T\) on the space of entire functions in \(d\) variables is called PDE-preserving for a given set \(\mathbb{P}\subseteq\mathbb{C}[\xi_1,\ldots,\xi_d]\) of polynomials if \(T\ker P(D)\subseteq P(D)\) for all \(P\in\mathbb P\), where \(P(D)\) is the differential operator obtained by replacing each variable \(\xi_j\) by ...
openaire   +1 more source

Spatial‐Wavelength Multiplexing Error‐Controlled Photonic Analog Computing System

Advanced Science, EarlyView.
A novel photonic integrated circuit prototype implementing the concept of general‐purpose analog computing and demonstrate its capability in radio frequency applications. The chip features a multichannel architecture and performs fully optical analog computation with frequency‐domain parallel processing. An FPGA‐based error‐correction algorithm aims to
Tao Zhu, Bowen Zhu, Shicheng Zhang, Keren Li, Xianchen Wu, Yazhi Pi, Jie Yan, Daigao Chen, Bingli Guo, Xi Xiao, Lei Wang, Xiaochuan Xu, Xuwei Xue, Shanguo Huang, Zizheng Cao, Shaohua Yu   +15 more
wiley   +1 more source