Investigating (non)-integrability and pulsating string in D3-brane background Rashmi R. Nayak, Kamal L. Panigrahi, Manoranjan Samal and Balbeer Singh Eur. Phys. J. C, 85 6 (2025) 670 Published online: 18 June 2025 DOI: 10.1140/epjc/s10052-025-14401-9