Results 31 to 40 of about 217,226 (371)
Equivalent transformations and exact solutions to the generalized cylindrical KdV type of equation
Nuclear Physics B, 2020 In this paper, by constructing equivalent transformations (ETs) of the generalized cylindrical KdV (cKdV) types of equations, we transform the variable-coefficient partial differential equations (vc-PDEs) into constant-coefficient PDEs (cc-PDEs) under ...
Hanze Liu +3 more
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Comments on whether nonlinear fractional partial differential equations have soliton solutions
Partial Differential Equations in Applied Mathematics, 2022 It is well known that many nonlinear integer-order partial differential equations (PDEs) have soliton solutions, this is an indisputable fact in the field of soliton theory.
Weiguo Rui
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Quantitative Predictive Modelling Approaches to Understanding Rheumatoid Arthritis: A Brief Review
Cells, 2019 Rheumatoid arthritis is a chronic autoimmune disease that is a major public health challenge. The disease is characterised by inflammation of synovial joints and cartilage erosion, which lead to chronic pain, poor life quality and, in some cases ...
Fiona R. Macfarlane +2 more
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Fast and Slow Decaying Solutions of Lane–Emden Equations Involving Nonhomogeneous Potential
Advanced Nonlinear Studies, 2020 Our purpose in this paper is to study positive solutions of the Lane–Emden ...
Chen Huyuan, Huang Xia, Zhou Feng
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Feynman-Kac representation of fully nonlinear PDEs and applications [PDF]
, 2014 The classical Feynman-Kac formula states the connection between linear parabolic partial differential equations (PDEs), like the heat equation, and expectation of stochastic processes driven by Brownian motion.
Pham, Huyen
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Communications in Computational Physics, 2020 Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encounted in computational science and engineering.
Yeonjong Shin, J. Darbon, G. Karniadakis
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A Rosetta Stone for information theory and differential equations
Communications in Advanced Mathematical Sciences, 2018 In this paper, we propose a dictionary between Partial Differential Equations and Information Theory. As a model case, we will discuss in detail the example of the Schrödinger Equation and Shannon Information Theory.
Alessandro Selvitella
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Unsupervised Legendre–Galerkin Neural Network for Solving Partial Differential Equations
IEEE Access, 2023 In recent years, machine learning methods have been used to solve partial differential equations (PDEs) and dynamical systems, leading to the development of a new research field called scientific machine learning, which combines techniques such as deep ...
Junho Choi, Namjung Kim, Youngjoon Hong
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Optimally weighted loss functions for solving PDEs with Neural Networks [PDF]
Journal of Computational and Applied Mathematics, 2020 Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks.
R. V. D. Meer, C. Oosterlee, A. Borovykh
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