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In the present Letter we present an analytical and numerical solution of theself-consistent mode-coupling equations for the problem of heat conductivity inone-dimensional systems. Such a solution leads us to propose a differentscenario to accomodate the known results obtained so far for this problem. Moreprecisely, we conjecture that the universality class is determined by theleading order of the nonlinear interaction potential. Moreover, our analysisallows us determining the memory kernel, whose expression puts on a more firmbasis the previously conjectured connection between anomalous heat conductivityand anomalous diffusion.Comment: Submitted to Physical Review

Self-consistent mode-coupling approach to one-dimensional heat transport