Results 21 to 30 of about 175 (58)
High order multiscale analysis of discrete integrable equations [PDF]
Open Communications in Nonlinear Mathematical PhysicsIn 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 +2 more
doaj +1 more source
, 2018 One class of nonhomogeneous neutral partial differential equations with deviating argument in the time variable is investigated. We find conditions under which it is possible to construct global solutions of these equations.
A. Samoilenko, L. M. Sergeeva
semanticscholar +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 +2 more
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 +2 more
doaj +1 more source
Differential Calculus on h-Deformed Spaces [PDF]
, 2017 We construct the rings of generalized differential operators on the ${\bf h}$-deformed vector space of ${\bf gl}$-type. In contrast to the $q$-deformed vector space, where the ring of differential operators is unique up to an isomorphism, the general ...
Herlemont, Basile, Ogievetsky, Oleg
core +5 more sources
Conservation laws of some lattice equations
, 2012 We derive infinitely many conservation laws for some multi-dimensionally consistent lattice equations from their Lax pairs. These lattice equations are the Nijhoff-Quispel-Capel equation, lattice Boussinesq equation, lattice nonlinear Schr\"{o}dinger ...
Cheng, Jun-wei, Zhang, Da-jun
core +1 more source
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
Multidimensional Toda Lattices: Continuous and Discrete Time [PDF]
, 2016 In this paper we present multidimensional analogues of both the continuous- and discrete-time Toda lattices. The integrable systems that we consider here have two or more space coordinates.
Aptekarev, Alexander I. +3 more
core +1 more source
A Completeness Study on Certain $2\times2$ Lax Pairs Including Zero Terms [PDF]
, 2011 We expand the completeness study instigated in [J. Math. Phys. 50 (2009), 103516, 29 pages] which found all $2\times2$ Lax pairs with non-zero, separable terms in each entry of each Lax matrix, along with the most general nonlinear systems that can be ...
Hay, Mike C.
core +4 more sources
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