2 research outputs found
Asymptotic dynamics of higher-order lumps in the Davey-Stewartson II equation
A family of higher-order rational lumps on non-zero constant background of Davey–Stewartson (DS) II equation are investigated. These solutions have multiple peaks whose heights and trajectories are approximately given by asymptotical analysis. It is found that the heights are time-dependent and for large time they approach the same constant height value of the first-order fundamental lump. The resulting trajectories are considered and it is found that the scattering angle can assume arbitrary values in the interval of which is markedly distinct from the necessary orthogonal scattering for the higher-order lumps on zero background. Additionally, it is illustrated that the higher-order lumps containing multi-peaked n-lumps can be regarded as a nonlinear superposition of n first-order ones as
Dispersionless limit of the noncommutative potential KP hierarchy and solutions of the pseudodual chiral model in 2+1 dimensions
The usual dispersionless limit of the KP hierarchy does not work in the case
where the dependent variable has values in a noncommutative (e.g. matrix)
algebra. Passing over to the potential KP hierarchy, there is a corresponding
scaling limit in the noncommutative case, which turns out to be the hierarchy
of a `pseudodual chiral model' in 2+1 dimensions (`pseudodual' to a hierarchy
extending Ward's (modified) integrable chiral model). Applying the scaling
procedure to a method generating exact solutions of a matrix (potential) KP
hierarchy from solutions of a matrix linear heat hierarchy, leads to a
corresponding method that generates exact solutions of the matrix
dispersionless potential KP hierarchy, i.e. the pseudodual chiral model
hierarchy. We use this result to construct classes of exact solutions of the
su(m) pseudodual chiral model in 2+1 dimensions, including various multiple
lump configurations.Comment: 37 pages, 10 figures, 2nd version: some extensions (Fig 3, Appendix
A, additional references), 3rd version: some minor changes, additional
reference