It is shown that the Calogero-Moser models based on all root systems of the finite reflection groups (both the crystallographic and non-crystallographic cases) with the rational (with/without a harmonic confining potential), trigonometric and hyperbolic potentials can be simply supersymmetrised in terms of superpotentials. There is a universal formula for the supersymmetric ground state wavefun...

In [1] new discretizations of the Euler top have been found. They can be discribed with a Lax pair with a spectral parameter on an elliptic curve. This is used in this paper to perform a finite gap integration .

In the paper [V. Adler, IMRN 1 (1998) 1–4] a lattice version of the Krichever-Novikov equation was constructed. We present in this note its Lax pair and discuss its elliptic form.

For periodic Toda chains with a large number N of particles we consider states which are N−2-close to the equilibrium and constructed by discretizing arbitrary given C2−functions with mesh size N−1. Our aim is to describe the spectrum of the Jacobi matrices LN appearing in the Lax pair formulation of the dynamics of these states as N → ∞. To this end we construct two Hill operators H± – such op...

as an application of hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. we have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear backlund transformations and construction of ...

We obtain conservation laws at negative regularity for the Benjamin-Ono equation on line and circle. These conserved quantities control $H^s$ norm of solution $-\frac{1}{2} < s 0$. The are obtained from a study perturbation determinant associated to Lax pair equation.

We prove a Tracy-Widom type formula for the generating function of occupancy numbers on several disjoint intervals higher order Airy point processes. The is related to new vector-valued Painlevé II hierarchy we define, together with its Lax pair.

We continue to study Lax (L-A, U-V) pairs (LP) joint covariance with respect to Darboux transformations (DT) as a classification principle. The scheme is based on a comparison of general expressions for the transformed coefficients of LP and its Frechet derivative. We use the compact expressions of the DT via some version of nonabelian Bell polynomials. It is shown that one more version of Bell...