The Viṣṇu-dharmottara describes that Lord Rāmacandra and His brothers - Lakṣmaṇa, Bharata and Śatrughna - are incarnations of Vāsudeva, Saṅkarṣaṇa, Pradyumna and Aniruddha respectively.
-Shrimad Bhagavatam Canto 5 Chapter 19 Verse 2 Purport

जन्म कर्म च मे दिव्यमेवं यो वेत्ति तत्त्वतः ।
त्यक्त्वा देहं पुनर्जन्म नैति मामेति सोऽर्जुन ॥ ९ ॥
One who knows the transcendental nature of My appearance and activities does not, upon leaving the body, take his birth again in this material world, but attains My eternal abode, O Arjuna.
-Bhagavad-Gita Chapter 4 Verse 9