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Linear Waves and Nonlinear Wave Interactions in a Bounded Three‐Layer Fluid System
Author(s) -
Weidman P. D.,
Nitsche M.,
Howard L.
Publication year - 2012
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/j.1467-9590.2011.00540.x
Subject(s) - bounded function , nonlinear system , physics , korteweg–de vries equation , soliton , rogue wave , mathematical analysis , energy (signal processing) , wave propagation , classical mechanics , mechanics , mathematics , optics , quantum mechanics
We investigate possible linear waves and nonlinear wave interactions in a bounded three‐layer fluid system using both analysis and numerical simulations. For sharp interfaces, we obtain analytic solutions for the admissible linear mode‐one parent/signature waves that exist in the system. For diffuse interfaces, we compute the overtaking interaction of nonlinear mode‐two solitary waves. Mathematically, owing to a small loss of energy to dispersive tails during the interaction, the waves are not solitons. However, this energy loss is extremely minute, and because the dispersively coupled waves in the system exhibit the three types of Lax KdV interactions, we conclude that for all intents and purposes the solitary waves exhibit soliton behavior.