We consider some special reductions of generic Darboux–Crum dressing formulae and of
their difference versions. As a matter of fact, we obtain some new formulae for Darboux …

We have already constructed solutions to the Kadomtsev-Petviashvili equation (KPI) in terms
of Fredholm determinants and wronskians of order 2N. These solutions have been called …

In this paper, we go on with the study of rational solutions to the Kadomtsev-Petviashvili
equation (KPI). We construct here rational solutions of order 5 as a quotient of 2 polynomials …

Here we constuct rational solutions of order 6 to the Kadomtsev-Petviashvili equation (KPI)
as a quotient of 2 polynomials of degree 84 in x, y and t depending on 10 parameters. We …

The Peregrine breather of order eleven (P 11 breather) solution to the focusing one-
dimensional nonlinear Schrödinger equation (NLS) is explicitly constructed here …

We go on with the study of the solutions to the focusing one dimensional nonlinear
Schrodinger equation (NLS). We construct here the thirteen's Peregrine breather (P13 …

For the famous Darboux‐Pöschl‐Teller equation, we present new wronskian representation
both for the potential and the related eigenfunctions. The simplest application of this new …

Quasi-rational solutions to the cylindrical nonlinear Schrödinger equation (CNLS) in terms of
wronskians and Fredholm determinants of order 2N depending on 2N− 2 real parameters …

We present a new proof of the integrability of the DDPT-I equation. The DDPT-I equation
represents a functional-difference deformation of the well-known Darboux–Pöschl–Teller …

Using a specific Darboux transformation, we construct solutions to the functional difference
KdV equation in terms of Casorati determinants. We give a complete description of the …