In the current work, we study the coupled Schrödinger–KdV (CS–KdV) equation. The Lie point symmetry generators are derived for the CS–KdV equation. We also show that the CS–KdV equation is nonlinearly self-adjoint and we use this property to construct conservation laws corresponding to the symmetries of the model. Symmetry reduction technique in conjunction with the extended tanh method is used to calculate the solitary wave solution. Also, conservation laws for the CS–KdV equation is derived by applying the new conservation theorem of Ibragimov. The undetermined coefficients and Bernoulli sub-ODE methods are suggested for constructing the topological, non-topological and singular soliton solutions to the model. New breather solitary solutions are constructed for CS–KdV equation by using bilinear form and the extended homoclinic test approach (EHTA).