We present a purely group-theoretical derivation of the continuous wavelet transform (CWT) on the 2-sphere S2, based on the construction of general coherent states associated to square integrable group representations. The parameter space X of our CWT is the product of SO(3) for motions and R+∗ for dilations on S2, which are embedded into the Lorentz group SO0(3,1) via the Iwasawa decomposition...

In a recent paper we constructed an integrable generalization of the Toda law on the square lattice. We construct other examples of integrable dynamics of Toda type on the square lattice, as well as on the triangular lattice, as nonlinear symmetries of the discrete Laplace equations on square and triangular lattices. We also construct the tau -function formulations and Darboux-Bäcklund transfor...

Abstract We analyse the Gaussian wave packet transform. Based on Fourier inversion formula and a partition of unity, which is formed by collection basis functions, new representation square-integrable functions presented. Including rigorous error analysis, variants transform are then derived discretization integral via different quadrature rules. Gauss–Hermite quadrature, we introduce packets i...