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On a 2+1‐Dimensional Whitham–Broer–Kaup System: A Resonant NLS Connection
Author(s) -
Rogers Colin,
Pashaev Oktay
Publication year - 2011
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.1467-9590.2010.00514.x
Subject(s) - integrable system , bilinear interpolation , one dimensional space , connection (principal bundle) , nonlinear system , mathematical physics , representation (politics) , schrödinger's cat , soliton , bilinear form , mathematical analysis , waves and shallow water , mathematics , physics , quantum mechanics , geometry , law , statistics , politics , political science , thermodynamics
It is established that the Whitham–Broer–Kaup shallow water system and the “resonant” nonlinear Schrödinger equation are equivalent. A symmetric integrable 2+1‐dimensional version of the Whitham–Broer–Kaup system is constructed which, in turn, is equivalent to a recently introduced resonant Davey–Stewartson I system incorporating a Madelung–Bohm type quantum potential. A bilinear representation is adopted and resonant solitonic interaction in this new 2+1‐dimensional Kaup–Broer system is exhibited.