Symmetry classification of the Gardner equation with time-dependent coefficients arising in stratified fluids

We perform symmetry classification of a variable-coefficient combined KdV–mKdV equation. That is, the equation combining the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations, or also known as the Gardner equation. The direct method of group classification is utilized to specify the forms of these time-dependent coefficients.