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We consider a two-component system of cubic semilinear wave equations in two space dimensions satisfying the Agemi-type structural condition (Ag) but violating (Ag0) and (Ag[Formula: see text]). For this system, we show that small amplitude solutions are asymptotically free as [Formula: see text].

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We consider the Cauchy problem for cubic nonlinear Klein-Gordon equations in one space dimension. We give the L p -decay estimate for the small data solution and show that it decays faster than the free solution if the cubic nonlinearity has the suitable dissipative structure.

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