An analytical exploration of dark and bright solitary wave solutions of time-fractional (3+1) -dimensional generalized Painlevé-type equation
Amer Alsulami
Scientific Reports, Published online: 06 May 2026; doi:10.1038/s41598-026-51692-8 An analytical exploration of dark and bright solitary wave solutions of time-fractional (3+1) -dimensional generalized Painlevé-type equation