On aspect of integrability, soliton, breather and positon solutions for the non-autonomous perturbed Gardner equation via Darboux transformation
摘要
A non-autonomous perturbed Gardner equation with soliton-type solutions is studied, along with some integrable features. Specifically, a Lax pair is generated for the said equation and applying the n-fold Darboux transformation, soliton, positons, breathers, and soliton interaction are displayed. Additionally, the amplitude and velocity of the soliton profile are expressed. To shed further light on the dynamic characteristics of the non-autonomous Gardner equation, this study presents hybrid solutions featuring various types of backgrounds. A comprehensive analysis of position solutions incorporating time-dependent phase shifts along with various dynamic characteristics is demonstrated. Based on the numerical understanding, the significant effect of perturbed and non-autonomous terms on the evolution of trajectory of the complete soliton profiles are analyzed.