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Construction of ( n + 1 ) $(n+1)$ -dimensional dual-mode nonlinear equations: multiple shock wave solutions for ( 3 + 1 ) $(3+1)$ -dimensional dual-mode Gardner-type and KdV-type

Crossref DOI link: https://doi.org/10.1186/s13662-019-1960-4

Published Online: 2019-01-22

Published Print: 2019-12

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

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