Conditional Lie–Bäcklund symmetries, differential constraints and new explicit solutions for the general nonlinear diffusion equations

Abstract

In this paper, based on the concepts of the conditional Lie–Bäcklund symmetry and the linear determining equations, the general nonlinear diffusion equations is discussed. And the results of classifying are displayed for such equations, it found that these equations preserve the second and third-order conditional Lie–Bäcklund symmetries. As a result, some new explicit solutions of these equations are presented.

Keywords

• Nonlinear diffusion equation
• Linear determining equation
• Differential constraints
• Conditional Lie–Bäcklund symmetry
• Explicit solution