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New exact optical solutions for the Lakshmanan–Porsezian–Daniel equation with parabolic law nonlinearity using the $$\phi ^{6}$$-expansion technique

Crossref DOI link: https://doi.org/10.1007/s11071-024-10430-3

Published Online: 2024-10-16

Published Print: 2025-03

Update policy: https://doi.org/10.1007/springer_crossmark_policy

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