TY - JOUR
T1 - Quasi-continuous spatial motion of a mass-spring chain
AU - Rosenau, Philip
PY - 1987/7
Y1 - 1987/7
N2 - The three-dimensional motion of mass-spring chain in close to continuum conditions (a large number of mass-springs per unit length) is shown to be governed by rtt= T(A) Ar5S+ h2 12rsstt, r=(x,y,z), A≡|rS|, where T is the tension function of the continuum (arbitrary but known) and A is the stretch, r is the spatial displacement vector, s is the reference coordinate along the chain and h is equilibrium discreteness length. Some exact solutions for the string (h≡0) and the chain are derived. While the string supports only trivial travelling waves (the stretch must be constant) the chain admits a travelling wave confined to a plane with the stretch propagating as a solitary wave. In general the dispersion born out of the discreteness counteracts the steepening of waves caused by the nonlinearity and leads to the formation of nonlinear structures.
AB - The three-dimensional motion of mass-spring chain in close to continuum conditions (a large number of mass-springs per unit length) is shown to be governed by rtt= T(A) Ar5S+ h2 12rsstt, r=(x,y,z), A≡|rS|, where T is the tension function of the continuum (arbitrary but known) and A is the stretch, r is the spatial displacement vector, s is the reference coordinate along the chain and h is equilibrium discreteness length. Some exact solutions for the string (h≡0) and the chain are derived. While the string supports only trivial travelling waves (the stretch must be constant) the chain admits a travelling wave confined to a plane with the stretch propagating as a solitary wave. In general the dispersion born out of the discreteness counteracts the steepening of waves caused by the nonlinearity and leads to the formation of nonlinear structures.
UR - http://www.scopus.com/inward/record.url?scp=45949123979&partnerID=8YFLogxK
U2 - 10.1016/0167-2789(87)90013-3
DO - 10.1016/0167-2789(87)90013-3
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AN - SCOPUS:45949123979
SN - 0167-2789
VL - 27
SP - 224
EP - 234
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 1-2
ER -