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On the Modulations and Nonlinear Interactions of Waves and the Nonlinear Stability of a Near‐Critical System
Author(s) -
Kennett Rosemary G.
Publication year - 1974
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 - 10.1002/sapm1974534317
Subject(s) - nonlinear system , perturbation (astronomy) , physics , mathematics , hagen–poiseuille equation , mathematical analysis , classical mechanics , flow (mathematics) , mechanics , quantum mechanics
The nonlinear interactions and modulations of an n ‐dimensional wave and of a disturbance to a near‐critical system governed by a general ( n + 1)‐dimensional system of equations are studied by perturbation methods. It is found that these modulations are governed by an evolution equation which is either by itself or coupled to a second equation, depending on the nature of the long wave solutions of the corresponding linearized system. When a single evolution equation exists, its leading terms are shown to give the nonlinear Schrödinger equation. Water waves and near‐critical plane Poiseuille flow are discussed as examples.