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A type of prolongation structure for several general systems is discussed. They are based on a set of one-forms in which the underlying structure group of the integrability condition corresponds to the Lie-algebra of SL (2,R), O(3), or…
The dynamics of Wilson loops are governed by an infinite set of Schwinger-Dyson equations and trace relations. In the context of the lattice positivity bootstrap, a central challenge is determining a dynamically independent basis of these…
In this article we present a Lagrangian representation for evolutionary systems with a Hamiltonian structure determined by a differential-geometric Poisson bracket of the first order associated with metrics of constant curvature.…
In this paper it is shown that the compact linearization approach, that has been previously proposed only for binary quadratic problems with assignment constraints, can be generalized to arbitrary linear equations with positive coefficients…
We show that when we formulate the lattice Boltzmann equation with a small time step $\Delta$t and an associated space scale $\Delta$x, a Taylor expansion joined with the so-called equivalent equation methodology leads to establish…
A generalized two-component model with peakon solutions is proposed in this paper. It allows an arbitrary function to be involved in as well as including some existing integrable peakon equations as special reductions. The generalized…
Hexagonal circle patterns are introduced, and a subclass thereof is studied in detail. It is characterized by the following property: For every circle the multi-ratio of its six intersection points with neighboring circles is equal to -1.…
The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…
We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…
Nonlinear perturbation of Fuchsian systems are studied in a region including two singularities. It is proved that such systems are generally not analytically equivalent to their linear part (they are not linearizable) and the obstructions…
We study fully nonlinear dead-core systems coupled with strong absorption terms. We discover a chain reaction, exploiting properties of an equation along the system and obtain higher sharp regularity across the free boundary. Additionally,…
We introduce a criterion that a given bihamiltonian structure allows a local coordinate system where both brackets have constant coefficients. This criterion is applied to the bihamiltonian open Toda lattice in a generic point, which is…
We consider systems of diffusion equations that have considerable interest in Soil Science and Mathematical Biology and focus upon the problem of finding those forms of this class that can be linearized. In particular we use the equivalence…
The discrete power function on the hexagonal lattice proposed by Bobenko et al is considered, whose defining equations consist of three cross-ratio equations and a similarity constraint. We show that the defining equations are derived from…
In this paper we study the existence of positive smooth solutions for a class of singular (p(x),q(x))- Laplacian systems by using sub and supersolution methods.
Binary symmetry constraints are applied to constructing B\"acklund transformations of soliton systems, both continuous and discrete. Construction of solutions to soliton systems is split into finding solutions to lower-dimensional Liouville…
A recurrence relation is said to have the Laurent property if all of its iterates are Laurent polynomials in the initial values with integer coefficients. We consider a family of nonlinear recurrences with the Laurent property, which were…
A previous article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs. They have infinite-dimensional Lie point symmetry groups…
Synchronization control of coupled continuous-time linear systems is studied. For identical systems that are stabilizable, a linear feedback law obtained via algebraic Riccati equation is shown to synchronize any fixed directed network of…
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of…