Psalm 43 is a short and anonymous, which is not uncommon in the Psalms. However, it is also the only psalm in the second volume that has no heading at all. This is one of three reasons that led many ancient compilers to combine Psalms 42-43 into just one psalm in old manuscripts. The second reason is the strong similarity to Psalm 42. A quick glance shows that the content of the two psalms is nearly identical – a prayer for vindication (Psalm 43:1), a cry for God’s attention (Psalm 43:2-3), and a burst of praise and thanksgiving for his response (Psalm 43:4).
Even more than all of that, though, is verse five. Psalm 43:5 is exactly the same refrain found in Psalm 42:5, 11. Thus, we find that this psalm (42-43) has three stanzas: 42:1-5; 42:6-11; 43:1-5.
See my post on Psalm 42 for more information on the meaning of this psalm.