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The spatiotemporal propagation behavior of a solitary wave is investigated ona Fermi-Pasta-Ulam ring. We observe the emergence of a cnoidal wave excited bythe solitary wave. The cnoidal wave may coexist with the solitary wave for along time associated with the periodic exchange of energy between these twononlinear waves. The module of the cnoidal wave, which is considered as anindicator of the nonlinearity, is found to oscillate with the same period ofthe energy exchange. After the stage of coexistence, the interaction betweenthese two nonlinear waves leads to the destruction of the cnoidal wave by theradiation of phonons. Finally, the interaction of the solitary wave withphonons leads to the loss of stability of the solitary wave.

Loss of stability of a solitary wave through exciting a cnoidal wave on a Fermi-Pasta-Ulam ring