Related papers: On some linear equations associated with dispersio…
We show how the superintegrability of certain systems can be deduced from the presence of multiple parameters in the rational Lax matrix representation. This is also related to the fact that such systems admit a separation of variables in…
A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known…
This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first…
A discrete system of coupled waves (with nonanalytic dispersion relation) is derived in the context of the spectral transform theory for the Ablowitz Ladik spectral problem (discrete version of the Zakharov-Shabat system). This 3-wave…
We study linearization models for continuous one-parameter semigroups of parabolic type. In particular, we introduce new limit schemes to obtain solutions of Abel's functional equation and to study asymptotic behavior of such semigroups.…
A new method is proposed to generate nonlinear integrable systems by starting with existing Lax pair and a new form of Kr\"onecker product. It is observed that such equation can be generated with the help of a Hamiltonian structure.…
A linear scaling method for calculation of the static {\em ab inito} response within self-consistent field theory is developed and applied to calculation of the static electric polarizability. The method is based on density matrix…
The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear…
In this paper, we consider the problem of piecewise affine abstraction of nonlinear systems, i.e., the overapproximation of its nonlinear dynamics by a pair of piecewise affine functions that "includes" the dynamical characteristics of the…
In a recent paper it was proposed that for some nonlinear shell models of turbulence one can construct a linear advection model for an auxiliary field such that the scaling exponents of all the structure functions of the linear and…
Completely integrable finite dimensional Hamiltonian systems are well understood thanks to the work of Liouville and Arnold. On the other hand, the Lax Pair formulation of the KdV equation marks the beginning of the extension of the…
Based on a PML for the advective wave equation, we propose two PML models for the linearized Euler equations. The derivation of the first model can be applied to other physical models. The second model was implemented. Numerical results are…
The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding…
The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation…
The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite 2D channel.…
The solution of constrained linear partial-differential equations can be described via parametric representations of linear relations. To study these representations, we provide a novel definition of boundary triplets for linear relations…
This is an introduction to advanced linear algebra, with emphasis on geometric aspects, and with some applications included too. We first review basic linear algebra, notably with the spectral theorem in its general form, and with the…
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be…
The intrinsic nature of a problem usually suggests a first suitable method to deal with it. Unfortunately, the apparent ease of application of these initial approaches may make their possible flaws seem to be inherent to the problem and…
Consider an ordinary differential equation which has a Lax pair representation A'(x)= [A(x),B(x)], where A(x) is a matrix polynomial with a fixed regular leading coefficient and the matrix B(x) depends only onA(x). Such an equation can be…