Vaishnava Samhita. Shri Vallabhacharya Charitam I. Vol III Book VII Chp 1 Shlokas 10 - 13

तदा वाराणसी सर्वा तुरुष्कैः पीडिताsभवत् |
दुद्राव ब्राह्मणः पत्न्या गर्भिण्या दुःखितो भृशम् ||
कृच्छ्रेण सञ्चरन् मार्गे चम्पारण्यमवाप सः |
निर्जने कानने घोरे न्यवसच्चिन्तयाssकुलः ||
तत्रैव सुषुवे पुत्रं सर्वलक्षणसम्युतम् |
शमीवृक्षसमीपे तु सती सा पावकप्रभम् ||
एकादश्यां कृष्णपक्षे वैशाखे मासि मङ्गले |
साक्षाद्वैश्वानरो लोके कृपयाsवततार ह ||   

At that time, Kashi was totally occupied by the mlecchas. Desperate Lakshmana Bhatta escaped along with his wife. With great difficulty he reached the Subrahmanya forest. He stayed in that dreadful and desolate forest with anxiety. Under a Vahni tree there, his wife gave birth to a baby who shone like Agnideva. Bhagavan Vaishvanara was born on this earth (in the form of that child) on the eleventh day from the full moon day in the Tamil month of Vaikashi (May - June)