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We consider Klein-Gordon models with a $\delta$-correlated spatial disorder.We show that the properties of immobile kinks exhibit strong dependence on theassumptions as to their statistical distribution over the minima of theeffective random potential. Namely, there exists a crossover from monotonicallyincreasing (when a kink occupies the deepest potential well) to thenon-monotonic (at equiprobable distribution of kinks over the potential minima)dependence of the average kink width as a function of the disorder intensity.We show also that the same crossover may take place with changing size of thesystem.Comment: 7 pages, 4 figure

Interplay of disorder and nonlinearity in Klein-Gordon models: Immobile kinks