In this article, we take into account the (1 + 1)-dimensional dispersive long-wave equation which is reduced from the Wu–Zhang equation. Firstly, the Bäcklund transformation and the non-local symmetry are successfully acquired from the truncated Painlevé expansion. At the same time, the non-local symmetry is transformed to Lie point symmetry by a suitable prolonged system. Then some solitary solutions are derived without a hitch via new Bäcklund transformation which originates from Lie point symmetry. Secondly, by utilising the consistent Riccati expansion method and the consistent tanh-expansion method, we find the interaction solutions between soliton and cnoidal wave by using the Jacobi elliptic function. Lastly, the conservation laws which are related to symmetries of the equation are successfully obtained by Ibragimov’s method.
Volume 95, 2021
Continuous Article Publishing mode
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