<p>This paper employs the method of dynamical systems to investigate the bifurcations and exact traveling wave solutions for a class of doubly sublinear Gardner equations. By analyzing the bifurcations in the phase portraits of the corresponding planar system under varying parameter conditions, we obtain a complete classification of all possible traveling wave solutions and examine the evolution of their profiles. Furthermore, we derive the exact representations of some right- and left-traveling compactons, which differ from those previously reported, and obtain new left-traveling periodic wave solutions. These results offer a deeper understanding of the doubly sublinear Gardner equation and valuable guidance for its theoretical and applied study.</p>