I do not think any one nation or people has a monopoly on grieving for their Dead and Fallen, in War or Peace. Before there was an official memorial day of any sort, widows and family of dead soldiers placed flowers on the graves of their loved ones. There is a desire to remember the Dead, especially if that person was very close to those left behind. This is not just true for the War Dead, and parents do grieve for children they must bury, at any age.
There is evidence that prehistoric men and women grieved for their Dead, based on items found at ancient burial sites.
So remember and Honor the Fallen, from whichever nation, and whichever date that official celebration occurs. The United States has chosen and designated the last Monday in May for that time of Honor. And one can do so privately, too, at any time.
from Wikipedia:
Memorial Day is a federal holiday in the United States for honoring the U.S. military personnel who died while serving in the U.S. Armed Forces.[1][2] It is observed on the last Monday of May.