A. Treibich & J.-L. Verdier, “Revêtements exceptionnels et sommes de 4 nombres triangulaires.”, Given a lattice L of the complex line, we consider the family of L-periodic functions decomposing as (twice) the sum of translates of the Weierstrass function by half-periods. We show they are all finite-gap potentials by constructing the corresponding spectral data. In particular, given such potential, we can read the main invariants of the corresponding spectral data, such as the genus as well as the corresponding theta-characteristic., Duke Mathematica Journal, 68:2 (1992), 217-236
A. Treibich, “Matrix Elliptic Solitons”, Following earlier work of I. Krichever & al., we consider the Matrix solutions to the KP equation, doubly periodic with respect to the first variable, and characterize and construct the corresponding spectral data, as irreducible divisors of a suitable ruled algebraic surface., Duke Mathematical Journal, 90:3 (1997), 523-547
A. Treibich, “Hyperelliptic tangential covers and elliptic finite-gap potentials”, We construct an explicit family of hyperelliptic tangential covers, equipped with specific theta-characteristics, giving rise to a new family of even elliptic finite-gap potentials (decomposing as twice the sum of translates of the Weierstrass function by half-periods, plus two extra terms)., Russian Mathematical Surveys, 56:6 (2001), 1107-1151
A. Treibich, “Hyperelliptic d-tangential covers and dxd Matrix KdV elliptic solitons”, We consider the dxd-matrix generalization of the KdV equation and construct spectral data, of arbitrary genus giving rise to elliptic dxd-matrix KdV solitons, i.e.: dxd-matrix KdV solutions doubly periodic with respect to the first variable., International Mathematics Research Notice, 2020:23 (2020), 9539-9558
А. Трейбич, “Касательные многочлены и эллиптические солитоны матричного уравнения Кортевега–де Фриза”, Функц. анализ и его прил., 50:4 (2016), 76–90; A. Treibich, “Tangential Polynomials and Matrix KdV Elliptic Solitons”, Funct. Anal. Appl., 50:4 (2016), 308–318
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