Abstract:
Using the differential geometry of curves and surfaces the Lakshmanan
equivalent counterpart of the M-XXII equation is found. It is shown that
these equations are too gauge eqivalent to each other. Also the gauge
equivalence between the Strachan and M-XXIIq equations is established.
Some integrals of motion are presented. It is well known that the spectral
parameter of the some (2+1)-dimensional soliton equations satisfies the
following equations: λt = κλnλy (a nonisospectral problems). We present
the simplest exact solutions of this equation.
