Interaction solutions for variable coefficient coupled Lakshmanan–Porsezian–Daniel equations via nonlocal residual symmetry and CTE method

After introducing a dependent transformation into the coupled Lakshmanan–Porsezian–Daniel equations with time-varying coefficients, we first obtain the residual symmetry in nonlocal structure for complex-valued functional equation via the truncated Painlevé expansion. Through localizing the nonlocal symmetry into the local Lie point symmetry, the interaction solutions between solitons and other coupled Lakshmanan–Porsezian–Daniel waves are constructed. Besides, by means of the consistent tanh function expansion (CTE) method, the interactions between solitons and elliptic periodic waves for variable coefficient coupled Lakshmanan–Porsezian–Daniel equations are derived. Finally, the controllable evolution behaviors of the interaction solutions are displayed in graphical way by fixing the variable wave parameters at some certain values.