Related papers: Integrable nonlinear field equations and loop alge…
Several families of nonlinear field equations are known to possess space- localized singularity-free solutions which describe fields with finite Hermitian norms. This paper studies the interaction of such fields with given electromagnetic…
New boundary conditions for integrable nonlinear lattices of the XXX type, such as the Heisenberg chain and the Toda lattice are presented. These integrable extensions are formulated in terms of a generic XXX Heisenberg magnet interacting…
The integrability of a system of two symmetrically coupled higher-order nonlinear Schr\"{o}dinger equations with parameter coefficients is tested by means of the singularity analysis. It is proven that the system passes the Painlev\'{e}…
In this work, we study some models of scalar fields in 1+1 dimensions with non-linear self-interactions. Here, we show how it is possible to extend the solutions recently reported in the literature for some classes of nonlinear equations…
Detailed mappings between zero-curvture equations for prolongation structures of nonlinear pde's and Estabrook-Wahlquist algorithms for same are given. The differences are exemplified by studies of the sine-Gordon equation. An example where…
We describe how the loop group maps corresponding to special submanifolds associated to integrable systems may be thought of as certain Grassmann submanifolds of infinite dimensional homogeneous spaces. In general, the associated families…
By employing supersymmetric quantum mechanics, we present a general algorithm to construct supersymmetric partner potentials and hence derive exact stationary solutions of the inhomogeneous nonlinear Schr\"odinger equation (INLSE). This is…
The local and non-local vector Non-linear Schrodinger Equation (NLSE) with a general cubic non-linearity are considered in presence of a linear term characterized, in general, by a non-hermitian matrix which under certain condition…
We extend to a specific class of systems of nonlinear Schr\"odinger equations (NLS) the theory of asymptotic stability of ground states already proved for the scalar NLS. Here the key point is the choice of an adequate system of modulation…
In the present contribution we consider a class of Schroedinger equations containing complex nonlinearities, describing systems with conserved norm $|\psi|^2$ and minimally coupled to an abelian gauge field. We introduce a nonlinear…
Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge-B\"acklund transformation, underlying symmetries among superficially…
We generalize the notion of semi-normalized classes of systems of differential equations, study properties of such classes and extend the algebraic method of group classification to them. In particular, we prove the important theorems on…
We consider a wide class of nonlinear canonical quantum systems described by a one-particle Schroedinger equation containing a complex nonlinearity. We introduce a nonlinear unitary transformation which permits us to linearize the…
Linear systems often involve, as a basic building block, solutions of equations of the form \begin{align*} A_Sx_S&+A_Px_P =0\\ A'_Sx_S & =0, \end{align*} where our primary interest might be in the vector variable $x_P.$ Usually, neither…
Integrable discretisations for a class of coupled (super) nonlinear Schrodinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are…
We propose and rigorously analyze a novel family of explicit low-regularity exponential integrators for the nonlinear Schr\"odinger (NLS) equation, based on a time-relaxation framework. The methods combine a resonance-based scheme for the…
The Calogero type matrix discretization scheme is applied to constructing the Lax type integrable discretizations of one wide enough class of nonlinear integrable dynamical systems on functional manifolds. Their Lie-algebraic structure and…
The construction of pointlike fields in quantum integrable models is usually approached by constructing their n-point functions. However, convergence questions of the resulting infinite series remain unresolved even in the simplest case of…
Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of a new class of integrable fractional…
This work is devoted to an integrable generalization of the nonlinear Schr\"odinger equation proposed by Fokas and Lenells. I discuss the relationships between this equation and other integrable models. Using the reduction of the…