This paper reviews breather, rogue, and interaction waves in a (3+1)-dimensional fourth-order nonlinear equation, deriving wave interactions and analyzing dynamics through graphical methods.
Discover the first rigorous error analysis of the Deep Ritz Method for solving elliptic PDEs. This work establishes nonasymptotic H1 convergence rates for Dirichlet, Neumann, and Robin boundary conditions, with clear guidance on optimal network depth and width.
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