Some properties for a new integrable soliton equation

In this paper, we introduce an integrable soliton equation and present its Lax pair and bi-Hamiltonian structure. We demonstrate that this integrable equation possesses special kink waves. The relationship between the integrable soliton equation and Gardner's equation is established by a reciprocal transformation. Our study extends previous research through a comparison between the soliton equation and its generalized version. (paper)