The Nile was the border of Egypt in those days. It served as the boundary and guard for Egypt's eastern border.
15:18-21 describes what is referred to in Jewish tradition as Gevulot Ha-aretz ("Borders of the Land") regarded as the full extent of the land promised to Abraham. Numbers 34:1-15 describes the land allocated to the Israelite tribes after the Exodus. The tribes of Reuben, Gad and half of Manasseh received land east of the Jordan as explained in Numbers 34:14-15. Numbers 34:1-13 provides a detailed description of the borders of the land allocated to the remaining tribes. The region is called "the Land of Canaan" (Eretz Kna'an) in Numbers 34:2 and the borders are known in Jewish tradition as the "borders for those coming out of Egypt". The English expression "Promised Land" can denote either the land promised to Abraham in Genesis or the land of Canaan, although the latter meaning is more common.
http://en.wikipedia.org/wiki/Land_of_Israel#The_Promised_Land
I haven't seen any map of Solomon's kingdom that him controlling the terrority to the Nile.
The maps in my Bible are not inspired. How ‘bout yours?
The promise in Gen 15:18 continues to describe the land as encompassing the nation of "the Kenites, the Kenezzites, the Kadmonites, the Hittites, the Perizzites, the Rephaim, the Amorites, the Canaanites, the Girgashites, and the Jebusites."
And how is it described in 1 Kings 4?
20 Judah and Israel were as numerous as the sand by the sea in multitude, eating and drinking and rejoicing. 21 So Solomon reigned over all kingdoms from the River to the land of the Philistines, as far as the border of Egypt. They brought tribute and served Solomon all the days of his life.Israel was a numerous as the sands of the seashore (part of the promise) and the land in question comprised all the kingdom listed in Gen.15:19.
And the context of the promise in Gen 15 is clearly regarding the time after they came out of exile in Egypt, not some unknown time far, far in the future ala dispensationalism (cf. vv.13,14).