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Initial/Boundary Value Problems for Simultaneous Evolution Equations in Three Dimensions
Author(s) -
Fokas A. S.,
Rogers C.
Publication year - 2001
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.1074192
Subject(s) - boundary value problem , mathematics , independent equation , mathematical analysis , nonlinear system , integrable system , simultaneous equations , initial value problem , numerical partial differential equations , differential equation , linear equation , physics , quantum mechanics
A novel procedure recently introduced by the senior author is adapted here for the analysis of initial/boundary value problems for pairs of linear dispersive evolution equations in three dimensions. Such simultaneous equations are shown to arise naturally out of linear representations for 2+1‐dimensional nonlinear integrable equations. The method presented emanates from the encoding of such simultaneous equations as the condition that a certain differential 1‐form is closed.