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Solving second-order nonlinear evolution partial differential equations using deep learning
Communications in Theoretical Physics, 2020Solving nonlinear evolution partial differential equations has been a longstanding computational challenge. In this paper, we present a universal paradigm of learning the system and extracting patterns from data generated from experiments.
J. Li 李, Y. Chen 陈
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Oberwolfach Reports, 2009
Following the successful pattern of the meeting in 2005, this year's workshop on 'Nonlinear Evolution Problems' focussed on a small number of currently very active areas in this field. By far the dominant theme, however, were geometric evolution equations of parabolic type, followed by the topic of wave equations and water waves ...
Klaus Ecker +2 more
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Following the successful pattern of the meeting in 2005, this year's workshop on 'Nonlinear Evolution Problems' focussed on a small number of currently very active areas in this field. By far the dominant theme, however, were geometric evolution equations of parabolic type, followed by the topic of wave equations and water waves ...
Klaus Ecker +2 more
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A connection between nonlinear evolution equations and ordinary differential equations of P‐type. II
Journal of Mathematical Physics, 1980M. Ablowitz, A. Ramani, H. Segur
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High-Order Nonlinear Evolution Equations
IMA Journal of Applied Mathematics, 1990The authors consider the higher order evolution equation of the form \[ \partial c/\partial t=\sum_{j=1}^ n\alpha_ j(\partial^ j/\partial x^ j)(c^{m_ j}). \] It is proved that this equation permits a similarity solution of the form \(c(x,t)=x^{-s}\phi(x/t^ q)\).
Hill, James M., Hill, Desmond L.
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Nonlinear evolution equations andH theorems
Journal of Statistical Physics, 1984zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alberti, Peter M., Crell, Bernd
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Computers and Mathematics with Applications, 2015
In this paper, the modified simple equation method (MSEM) is applied to construct exact solutions of the generalized ( 2 + 1 )-dimensional nonlinear evolution equations (NLEEs) involving parameters via the ( 2 + 1 )-dimensional Calogero-Bogoyavlenskii ...
Mohammed O. Al-Amr
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In this paper, the modified simple equation method (MSEM) is applied to construct exact solutions of the generalized ( 2 + 1 )-dimensional nonlinear evolution equations (NLEEs) involving parameters via the ( 2 + 1 )-dimensional Calogero-Bogoyavlenskii ...
Mohammed O. Al-Amr
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A Stochastic Nonlinear Evolution Equation
Zeitschrift für Analysis und ihre Anwendungen, 1992A stochastic evolution equation for processes with values in two orthogonal subspaces of a Hilbert space is considered. Such types of equations arise in the study of quasistatic processes of elastic viscoplastic materials with random disturbances. Using the theory of Hilbert space valued Ito equations an existence and uniqueness theorem is proved ...
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DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS
Chinese Annals of Mathematics, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ma, Tian, Wang, Shouhong
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Nonlinear evolution equations and nonlinear ergodic theorems
Nonlinear Analysis: Theory, Methods & Applications, 1977Publisher Summary This chapter discusses nonlinear evolution equations and nonlinear ergodic theorems. It discusses certain aspects of the asymptotic behavior of generalized solutions of nonlinear evolution equations and of nonlinear nonexpansive semigroups in Banach spaces.
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