## Abstract

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 r_{tt}= T(A) Ar_{5S}+ h^{2} 12r_{sstt}, r=(x,y,z), A≡|r_{S}|, 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.

Original language | English |
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Pages (from-to) | 224-234 |

Number of pages | 11 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 27 |

Issue number | 1-2 |

DOIs | |

State | Published - Jul 1987 |

Externally published | Yes |