Symmetries and conservation laws of lattice Boussinesq equations
Pavlos Xenitidis, Frank Nijhoff
TL;DR
This paper derives conservation laws and symmetries for lattice Boussinesq systems, constructs related hierarchies and Lax pairs, and connects them to integrable PDEs via symmetry reduction.
Contribution
It introduces new hierarchies of symmetries and conservation laws for lattice Boussinesq equations and links discrete systems to continuous integrable PDEs.
Findings
Derived sequences of conservation laws and symmetries.
Constructed hierarchies of differential-difference equations.
Connected lattice systems to integrable PDEs through symmetry reduction.
Abstract
Sequences of canonical conservation laws and generalized symmetries for the lattice Boussinesq and the lattice modified Boussinesq systems are successively derived. The interpretation of these symmetries as differential-difference equations leads to corresponding hierarchies of such equations for which conservation laws and Lax pairs are constructed. Finally, using the continuous symmetry reduction approach, an integrable, multidimensionally consistent system of partial differential equations is derived in relation with the lattice modified Boussinesq system.
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