Journal
SYMMETRY-BASEL
Volume 13, Issue 6, Pages -Publisher
MDPI
DOI: 10.3390/sym13061008
Keywords
Lagrange lattice; continualization; Debye's quasicontinuum; phase velocity; group velocity; quasifront; asymptotics; change of symmetry
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This paper compares the asymptotic behaviors of wave solutions describing discrete lattice motion and its continuous approximations. The transition from discrete to continuous medium changes system symmetry, impacting wave asymptotics. Analyzing phase and group velocities, the study evaluates the merits and limitations of various continuous approximations in different time scales.
This paper is devoted to comparing the asymptotics of a solution, describing the wave motion of a discrete lattice and its continuous approximations. The transition from a discrete medium to a continuous one changes the symmetry of the system. The influence of this change on the asymptotic behavior of waves is of great interest. For the discrete case, Schrodinger's analytical solution of the initial-value problem for the Lagrange lattice is used. Various continuous approximations are proposed to approximate the lattice. They are based on Debye's concept of quasicontinuum. The asymptotics of the initial motion and the behavior of the systems in the vicinity of the quasifront and at large times are compared. The approximations of phase and group velocities is analyzed. The merits and limitations of the described approaches are discussed.
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