Related papers: Recursion Operators of Some Equations of Hydrodyna…

Three new iteration methods, namely the squared-operator method, the modified squared-operator method, and the power-conserving squared-operator method, for solitary waves in general scalar and vector nonlinear wave equations are proposed.…

The particular case of the integrable two component (2+1)-dimensional hydrodynamical type systems, which generalises the so-called Hamiltonian subcase, is considered. The associated system in involution is integrated in a parametric form. A…

The universal field equations introduced by the author and his collaborators, which admit infinitely many inequivalent Lagrangian formulations are shown to arise as consistency conditions for the existence of non-trivial solutions to the…

We present a unified framework to construct well-posed formulations for large classes of linear operator equations including elliptic, parabolic and hyperbolic partial differential equations. This general approach incorporates known weak…

In the realm of relativistic astrophysics, the ideal equation of state with a constant adiabatic index provides a poor approximation due to its inconsistency with relativistic kinetic theory. However, it is a common practice to use it for…

We present the Lax operator for the N=3 KdV hierarchy and consider its extensions. We also construct a new infinite family of N=2 supersymmetric hierarchies by exhibiting the corresponding super Lax operators. The new realization of N=4…

The relativistic method of moments is one of the most successful approaches to extract second order viscous hydrodynamics from a kinetic underlying background. The equations can be systematically improved to higher order, and they have…

In this paper we present a systematic study of regular sequences of quasi-nonexpansive operators in Hilbert space. We are interested, in particular, in weakly, boundedly and linearly regular sequences of operators. We show that the type of…

We consider hydrodynamic scaling limits for a class of reversible interacting particle systems, which includes the symmetric simple exclusion process and certain zero-range processes. We study a (non-quadratic) microscopic action functional…

We find direct and inverse recursion operators for integrable cases of the rmdKP and rdDym equations. Also, we study actions of these operators on the contact symmetries and find shadows of nonlocal symmetries of these equations.

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

We prove various Beurling-Lax type theorems, when the classical backward-shift operator is replaced by a general resolvent operator associated with a rational function. We also study connections to the Cuntz relations. An important tool is…

Simple, self-similar, analytic solutions of (1+3)-dimensional relativistic hydrodynamics are presented for ellipsoidally symmetric finite fireballs corresponding to non-central collisions of heavy ions at relativistic bombarding energies.…

We construct the recursion operators for the non-commutative Burgers equations using their Lax operators. We investigate the existence of any integrable mixed version of left- and right-handed Burgers equations on higher symmetry grounds.

For one dimensional SU(n) Hubbard model, a pair of Lax operators are derived, which give a set of fundamental equations for the quantum inverse scattering method under both periodic and open boundary conditions. This provides another proof…

We extend the reduction group method to the Lax-Darboux schemes associated with nonlinear Schr\"odinger type equations. We consider all possible finite reduction groups and construct corresponding Lax operators, Darboux transformations,…

We give a pedagogical review of relativistic hydrodynamics relevant to relativistic heavy ion collisions. Topics discussed include linear response theory derivation of 2nd order viscous hydrodynamics including the Kubo formulas, kinetic…

An explicit expression for the Dirichlet-Neumann operator for surface water waves is presented. For non-overturning waves, but without assuming small amplitudes, the formula is first derived in two dimensions, subsequently extrapolated in…

Algorithms for the symbolic computation of conserved densities, fluxes, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations are presented. In the algorithms we use discrete versions of…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…