### Abstract

This is the second part of a two‐part series on forced lattice vibrations in which a semi‐infinite lattice of one‐dimensional particles {x_{n}}_{n≧1}, (Formula Presented.) is driven from one end by a particle x_{0}. This particle undergoes a given, periodically perturbed, uniform motion x0(t) = 2at + h(yt) where a and γ are constants and h(·) has period 2π. Results and notation from Part I are used freely and without further comment. Here the authors prove that sufficiently ample families of traveling‐wave solutions of the doubly infinite system (Formula Presented.) exist in the cases γ > γ_{1} and γ_{1} > γ > γ_{2} for general restoring forces F. In the case with Toda forces, F(x) = e^{x}, the authors prove that sufficiently ample families of traveling‐wave solutions exist for all k, γ_{k} > γ > γ_{k+1}. By a general result proved in Part I, this implies that there exist time‐periodic solutions of the driven system (i) with k‐phase wave asymptotics in n of the type (Formula Presented.) with k = 0 or 1 for general F and k arbitrary for F(x) = e^{x} (when k = 0, take γ_{0} = ∞ and X_{0} ≡ 0).

Original language | English (US) |
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Pages (from-to) | 1251-1298 |

Number of pages | 48 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 48 |

Issue number | 11 |

DOIs | |

State | Published - 1995 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*48*(11), 1251-1298. https://doi.org/10.1002/cpa.3160481103