TY - JOUR

T1 - A model equation for wavepacket solitary waves arising from capillary-gravity flows

AU - Akers, Benjamin

AU - Milewski, Paul A

PY - 2009/4

Y1 - 2009/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=63849192481&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1111/j.1467-9590.2009.00432.x

U2 - 10.1111/j.1467-9590.2009.00432.x

DO - 10.1111/j.1467-9590.2009.00432.x

M3 - Article

VL - 122

SP - 249

EP - 274

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

IS - 3

ER -