Extra Dimensions and Nonlinear Equations
Thomas Curtright, David Fairlie
TL;DR
This paper introduces a dimension-doubling method to linearize and solve nonlinear multi-component Euler-Monge PDEs in multiple dimensions, revealing nonlocal structures and a boundary-bulk interpretation.
Contribution
The paper presents a novel dimension-doubling technique that fully linearizes nonlinear Euler-Monge equations and uncovers their boundary-bulk relationship.
Findings
Complete linearization of nonlinear PDEs achieved
Identification of nonlocal structures in solutions
Boundary theory interpretation from bulk linear system
Abstract
Solutions of nonlinear multi-component Euler-Monge partial differential equations are constructed in n spatial dimensions by dimension-doubling, a method that completely linearizes the problem. Nonlocal structures are an essential feature of the method. The Euler-Monge equations may be interpreted as a boundary theory arising from a linearized bulk system such that all boundary solutions follow from simple limits of those for the bulk.
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