Results 31 to 40 of about 183 (76)

Diffraction on the Two-Dimensional Square Lattice [PDF]

, 2009
We solve the thin-slit diffraction problem for two-dimensional lattice waves. More precisely, for the discrete Helmholtz equation on the semi-infinite square lattice with data prescribed on the left boundary (the aperture), we use lattice Green's ...
Bhat, H. S., Osting, Braxton
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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

Characteristics of Conservation Laws for Difference Equations [PDF]

, 2013
Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the ...
A. Mikhailov, A.G. Rasin, A.G. Rasin, A.V. Mikhailov, B.A. Kupershmidt, J. Hietarinta, L. Arriola, L. Martínez Alonso, O.G. Rasin, O.G. Rasin, O.G. Rasin, O.G. Rasin, P.E. Hydon, P.E. Hydon, P.E. Hydon, P.J. Olver, Peter E. Hydon, R. Hirota, S.C. Anco, S.C. Anco, Timothy J. Grant, V.A. Dorodnitsyn, V.A. Dorodnitsyn, V.E. Adler   +23 more
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Discrete integrable systems generated by Hermite-Pad\'e approximants

, 2015
We consider Hermite-Pad\'e approximants in the framework of discrete integrable systems defined on the lattice $\mathbb{Z}^2$. We show that the concept of multiple orthogonality is intimately related to the Lax representations for the entries of the ...
Aptekarev, Alexander I., Derevyagin, Maxim, Van Assche, Walter   +2 more
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A varA variational principle for discrete integrable systemsiational principle for discrete integrable systems [PDF]

, 2018
For integrable systems in the sense of multidimensional consistency (MDC) we can consider the Lagrangian as a form, which is closed on solutions of the equations of motion.
Lobb, SB, Nijhoff, FW
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Homoclinic solutions in periodic partial difference equations

Advances in Nonlinear Analysis
By using critical point theory in combination with periodic approximations, we obtain novel sufficient conditions for the existence of nontrivial homoclinic solutions for a class of periodic partial difference equations with sign-changing mixed ...
Mei Peng, Zhou Zhan, Yu Jianshe
doaj   +1 more source

Hirota equation and the quantum plane

, 2012
We discuss geometric integrability of Hirota's discrete KP equation in the framework of projective geometry over division rings using the recently introduced notion of Desargues maps.
Doliwa, Adam
core   +1 more source

Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models [PDF]

, 2013
The mathematical structure of homogeneous loop quantum cosmology is analyzed, starting with and taking into account the general classification of homogeneous connections not restricted to be Abelian.
Bojowald, Martin
core   +3 more sources

A variational perspective on continuum limits of ABS and lattice GD equations

, 2019
A pluri-Lagrangian structure is an attribute of integrability for lattice equations and for hierarchies of differential equations. It combines the notion of multi-dimensional consistency (in the discrete case) or commutativity of the flows (in the ...
Vermeeren, Mats
core   +1 more source

Percival Lagrangian approach to Aubry-Mather theory [PDF]

, 2011
We present some streamlined proofs of some of the basic results in Aubry-Mather theory (existence of quasi-periodic minimizers, multiplicity results when there are gaps among minimizers) based on the study of hull functions.
De La Llave, Rafael, Xifeng Su
core