4 papers · 1 filter
Quasi-classical $\dbar$-method: Generating equations for dispersionless integrable hierarchies
L. V. Bogdanov, B. G. Konopelchenko, L. Martinez Alonso
The quasi-classical -dressing method is used to derive compact generating equations for dispersionless hierarchies. Dispersionless Kadomtsev-Petviashvili (KP) and t…
Reciprocal figures, graphical statics and inversive geometry of the Schwarzian BKP hierarchy
B. G. Konopelchenko, W. K. Schief
A remarkable connection between soliton theory and an important and beautiful branch of the theory of graphical statics developed by Maxwell and his contemporaries is revealed. Thu…
On the unification of classical and novel integrable surfaces: I. Differential geometry
W. K. Schief, B. G. Konopelchenko
A novel class of integrable surfaces is recorded. This class of O surfaces is shown to include and generalize classical surfaces such as isothermic, constant mean curvature, minima…
dbar-approach to the dispersionless KP hierarchy
B. Konopelchenko, L. Martinez Alonso, O. Ragnisco
The dispersionless limit of the scalar nonlocal dbar-problem is derived. It is given by a special class of nonlinear first-order equations. A quasi-classical version of the dbar-dr…