Abstract
This paper is concerned with the bifurcation phenomenon of large amplitude periodic solutions of coupled nonlinear wave equations with either constant or variable coefficients. Such model arises when two waves propagate simultaneously in nonisotropic media. The change of degree argument is used to obtain necessary and sufficient conditions for the existence of asymptotic bifurcation points with respect to the matrix spectrum. The results we get are also valid for uncoupled systems. By changing one of our assumptions on the nonlinear term, we also obtain the necessary and sufficient conditions for the existence of the standard bifurcation points.
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