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A Model Equation for Wavepacket Solitary Waves Arising from Capillary‐Gravity Flows
Author(s) -
Akers Benjamin,
Milewski Paul A.
Publication year - 2009
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.1467-9590.2009.00432.x
Subject(s) - wave packet , physics , dispersion relation , wave propagation , wavenumber , classical mechanics , dispersion (optics) , nonlinear system , transverse plane , gravity wave , mechanics , optics , quantum mechanics , structural engineering , engineering
A model equation governing the primitive dynamics of wave packets near an extremum of the linear dispersion relation at finite wavenumber is derived. In two spatial dimensions, we include the effects of weak variation of the wave in the direction transverse to the direction of propagation. The resulting equation is contrasted with the Kadomtsev–Petviashvilli and Nonlinear Schrödinger (NLS) equations. The model is derived as an approximation to the equations for deep water gravity‐capillary waves, but has wider applications. Both line solitary waves and solitary waves which decay in both the transverse and propagating directions—lump solitary waves—are computed. The stability of these waves is investigated and their dynamics are studied via numerical time evolution of the equation.