All bell- and kink-shaped solitons sustained by an infinite periodic atomic chain of arbitrary anharmonicity are worked out by solving a second-order, nonlinear differential equation involving advanced and retarded terms. The asymptotic time decay behaves exponentially or as a power law according to whether the potential has a harmonic limit or not. Excellent agreement is achieved with Toda's model. Illustrative examples are also given for the Fermi-Pasta-Ulam and sine-Gordon potentials. Lattice and continuum solitons differ markedly from one another.

• Received 2 April 1999

DOI:https://doi.org/10.1103/PhysRevLett.83.3982