Deriving conservation laws for ABS lattice equations from Lax pairs

In this paper we derive infinitely many conservation laws for ABS lattice equations from their Lax pairs. These conservation laws can be algebraically expressed by means of some known polynomials. For each equation, the infinitely many conservation laws are not equivalent and are nontrivial. We also...

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Published inJournal of physics. A, Mathematical and theoretical Vol. 46; no. 26; pp. 265202 - 19
Main Authors Zhang, Da-jun, Cheng, Jun-wei, Sun, Ying-ying
Format Journal Article
LanguageEnglish
Published IOP Publishing 05.07.2013
Subjects
ABS
ABS lattice equations
Algebra
Conservation laws
discrete integrable systems
Equivalence
Lattices
Lax pairs
Lists
Mathematical analysis
Polynomials
Riccati equation
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Summary:In this paper we derive infinitely many conservation laws for ABS lattice equations from their Lax pairs. These conservation laws can be algebraically expressed by means of some known polynomials. For each equation, the infinitely many conservation laws are not equivalent and are nontrivial. We also show that the (H1), (H2), (H3), (Q1), (Q2), (Q3) and (A1) equations in the ABS list share a generic discrete Riccati equation.
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ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/46/26/265202