9 research outputs found
Building extended resolvent of heat operator via twisting transformations
Twisting transformations for the heat operator are introduced. They are used,
at the same time, to superimpose a` la Darboux N solitons to a generic smooth,
decaying at infinity, potential and to generate the corresponding Jost
solutions. These twisting operators are also used to study the existence of the
related extended resolvent. Existence and uniqueness of the extended resolvent
in the case of solitons with N "ingoing" rays and one "outgoing" ray is
studied in details.Comment: 15 pages, 2 figure
On the equivalence of different approaches for generating multisoliton solutions of the KPII equation
The unexpectedly rich structure of the multisoliton solutions of the KPII
equation has been explored by using different approaches, running from dressing
method to twisting transformations and to the tau-function formulation. All
these approaches proved to be useful in order to display different properties
of these solutions and their related Jost solutions. The aim of this paper is
to establish the explicit formulae relating all these approaches. In addition
some hidden invariance properties of these multisoliton solutions are
discussed
The Cauchy Problem for the Kadomtsev–Petviashili II Equation with Nondecaying Data along a Line
Multiparametric Families of Solutions of the Kadomtsev–Petviashvili-I Equation, the Structure of Their Rational Representations, and Multi-Rogue Waves
The three wave resonant interaction equations: spectral and numerical methods
The spectral theory of the integrable partial differential equations which model the resonant interaction of three waves is considered with the purpose of numerically solving the direct spectral problem for both vanishing and non vanishing boundary values.
Methods of computing both the continuum spectrum data and the discrete spectrum eigenvalues are given together with examples of such computations. The explicit spectral representation of the Manley-Rowe invariants is also displayed