TY - JOUR
T1 - Dynamics of dense lattices
AU - Rosenau, Philip
PY - 1987
Y1 - 1987
N2 - We derive the equations governing the nonlinear dynamics of one-, two-, and three-dimensional lattices in a close to continuum condition (i.e., a dense lattice). The described method correctly captures all terms to a given order in discreteness and, unlike previous approaches, leads to well-behaved partial-differential equations for these problems. In general, the dispersion born out of discreteness counteracts the steepening of waves caused by the nonlinearity and leads to the formation of permanent nonlinear structures.
AB - We derive the equations governing the nonlinear dynamics of one-, two-, and three-dimensional lattices in a close to continuum condition (i.e., a dense lattice). The described method correctly captures all terms to a given order in discreteness and, unlike previous approaches, leads to well-behaved partial-differential equations for these problems. In general, the dispersion born out of discreteness counteracts the steepening of waves caused by the nonlinearity and leads to the formation of permanent nonlinear structures.
UR - http://www.scopus.com/inward/record.url?scp=25344474267&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.36.5868
DO - 10.1103/PhysRevB.36.5868
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AN - SCOPUS:25344474267
SN - 1098-0121
VL - 36
SP - 5868
EP - 5876
JO - Physical Review B-Condensed Matter
JF - Physical Review B-Condensed Matter
IS - 11
ER -