Nonlocal symmetry, exact solutions and conservation laws of the (1+1)-dimensional Levi equation

Residual symmetry, CRE integrability and interaction solutions of two higher-dimensional shallow water wave equations

“…To obtain more generalized solutions, Lou [21] generalized the Riccati expansion method to the consistent Riccati expansion (CRE) method, through which a new integrable property called the CRE integrable is defined and new interaction solutions between solitons and periodic waves are generated for many nonlinear equations. [22][23][24][25][26][27][28] The observation of solitons interacting with periodic background waves has been documented in experimental studies. [29] In this paper, using residual symmetry and the CRE method, we focus on two (3 + 1)-dimensional shallow water wave equations as follows: [30]…”