Abstract
We investigate certain properties of -valued two-dimensional (2D) soliton surfaces associated with the integrable sigma models constructed by orthogonal rank-one Hermitian projectors, which are defined on the 2D Riemann sphere with a finite action functional. Several new properties of the projectors mapping onto one-dimensional subspaces, as well as their relations with three mutually different immersion formulas, namely, the generalized Weierstrass, Sym–Tafel and Fokas–Gelfand, have been discussed in detail. Explicit connections among these three surfaces are also established by purely analytical descriptions, and it is demonstrated that the three immersion formulas actually correspond to the single surface parametrized by some specific conditions.
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