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Applications to Partial Differential Equations—Nonlinear Equations
1983In this section we consider a simple application of the results of Section 6.1 to the initial value problem for the following nonlinear Schrodinger equation in ∝2 $$\left\{ {_{u(x,0) = {u_0}(x)in{\mathbb{R}^2}}^{\frac{1}{i}\frac{{\partial u}}{{\partial t}} - \Delta u + k{{\left| u \right|}^2}u = 0in]0,\infty [x{\mathbb{R}^2}}} \right.$$ (1.1 ...
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Partial differential equations with differential constraints
1997A. Grundland, MARTINA, Luigi, G. Rideau
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HYPERGEOMETRIC PARTIAL DIFFERENTIAL EQUATIONS (II)
The Quarterly Journal of Mathematics, 1935openaire +2 more sources
The Painlevé property for partial differential equations
Journal of Mathematical Physics, 1983Weiss John
exaly
Solving high-dimensional partial differential equations using deep learning
Proceedings of the National Academy of Sciences of the United States of America, 2018Jiequn Han, Arnulf Jéntzen, Weinan E
exaly
Classification of Partial Differential Equations
Journal of the Society for Industrial and Applied Mathematics, 1954openaire +2 more sources