I have located a memorial on Find A Grave for Helene M. Petersen (b. Oct. 29, 1887 d. Aug. 24, 1965). In fact, I have very recently come manage her memorial and was trying to "reunite" her with family.
Her memorial number is #42870069.
If this Helene does indeed match your Peter, that would mean he lived beyond her 18 years, so maybe he remarried.
Beyond that, I have delved into the Petersen family a good deal today, and in doing so, I have run into several references to Peter Petersen around the Omaha / Washington / Dodge county area. Washington County Historical Society has a site you may wish to check out (free check on marriages), but I am afraid Peter Petersen is not exactly an uncommon name.