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Initial Time Layers and Kadomtsev–Petviashvili‐Type Equations
Author(s) -
Ablowitz Mark J.,
Wang XiaoPing
Publication year - 1997
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 - 10.1111/1467-9590.00043
Subject(s) - classification of discontinuities , limit (mathematics) , mathematics , context (archaeology) , mathematical analysis , kadomtsev–petviashvili equation , type (biology) , partial differential equation , characteristic equation , geology , paleontology
The Kadomtsev–Petviashvili (KP) equation and generalizations (GKP) have temporal discontinuities at the initial instant of time. Motivated by the study of water waves, a generalized Boussinesq equation that contains the GKP equations as an “outer” limit is introduced. Within the context of matched asymptotic expansions the discontinuities are resolved. The linear system is analyzed in more detail and the limit process is rigorously established.