Results 11 to 20 of about 183 (76)

Two-Dimensional Toda-Heisenberg Lattice [PDF]

, 2013
We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear system, which ...
Vekslerchik, Vadim E.
core   +4 more sources

Multiple solutions for a class of oscillatory discrete problems

Advances in Nonlinear Analysis, 2015
In this paper, we study a discrete nonlinear boundary value problem that involves a nonlinear term oscillating at infinity and a power-type nonlinearity up.
Mălin Maria
doaj   +1 more source

Yang-Baxter Maps from the Discrete BKP Equation [PDF]

, 2010
We construct rational and piecewise-linear Yang-Baxter maps for a general N-reduction of the discrete BKP ...
Kakei, Saburo, Nimmo, Jonathan J. C., Willox, Ralph   +2 more
core   +6 more sources

A study on the domain independence of the Laurent property, the irreducibility and the coprimeness in lattice equations [PDF]

Open Communications in Nonlinear Mathematical Physics
We study the Laurent property, the irreducibility and the coprimeness for lattice equations (partial difference equations), mainly focusing on how the choice of initial value problem (the choice of domain) affects these properties.
Takafumi Mase
doaj   +1 more source

Symmetries of the Hirota Difference Equation [PDF]

, 2017
Continuous symmetries of the Hirota difference equation, commuting with shifts of independent variables, are derived by means of the dressing procedure. Action of these symmetries on the dependent variables of the equation is presented.
Pogrebkov, Andrei K.
core   +3 more sources

Non-commutative lattice modified Gel'fand-Dikii systems [PDF]

, 2013
We introduce integrable multicomponent non-commutative lattice systems, which can be considered as analogs of the modified Gel'fand-Dikii hierarchy. We present the corresponding systems of Lax pairs and we show directly multidimensional consistency of ...
Doliwa, Adam
core   +1 more source

High order multiscale analysis of discrete integrable equations [PDF]

Open Communications in Nonlinear Mathematical Physics
In this article we present the results obtained applying the multiple scale expansion up to the order $\varepsilon^6$ to a dispersive multilinear class of equations on a square lattice depending on 13 parameters. We show that the integrability conditions
Rafael Hernandez Heredero, Decio Levi, Christian Scimiterna   +2 more
doaj   +1 more source

Non-Point Invertible Transformations and Integrability of Partial Difference Equations [PDF]

, 2014
This article is devoted to the partial difference quad-graph equations that can be represented in the form $\varphi (u(i+1,j),u(i+1,j+1))=\psi (u(i,j),u(i,j+1))$, where the map $(w,z) \rightarrow (\varphi(w,z),\psi(w,z))$ is injective. The transformation
Startsev, Sergey Ya.
core   +2 more sources

Linearizability of Nonlinear Equations on a Quad-Graph by a Point, Two Points and Generalized Hopf-Cole Transformations [PDF]

, 2011
In this paper we propose some linearizability tests of partial difference equations on a quad-graph given by one point, two points and generalized Hopf-Cole transformations.
Levi, Decio, Scimiterna, Christian
core   +4 more sources

Well-posedness and maximum principles for lattice reaction-diffusion equations

Advances in Nonlinear Analysis, 2017
Existence, uniqueness and continuous dependence results together with maximum principles represent key tools in the analysis of lattice reaction-diffusion equations.
Slavík Antonín, Stehlík Petr, Volek Jonáš   +2 more
doaj   +1 more source