The non-autonomous generalized perturbed KdV equation: its integrability, infinite conservation laws, multi soliton, high-order breather and hybrid solutions with mixed backgrounds

Abstract This paper claims the integrability of the non-autonomous generalized perturbed KdV (NgPKdV) equation through Painlevé analysis. Additionally, bilinear Bäcklund transformations, Lax pairs, and infinite conservation laws are developed to demonstrate the integrability of the said equation. Employing Hirota's approach, multi-solitons of the NgPKdV equation are constructed, from which the breather and hybrid solutions are explored with the proper choice of polynomial functions in the solution space. The changes in the behavior of non-autonomous solitons under different physical conditions are studied with special care. The propagating properties of single and double non-autonomous breathers along with their interactive properties with solitons are observed from the numerical viewpoint. An extensive study is also conducted on the propagation of solitary interactions and complex hybrid solutions. PACS 52.30-q · 94.30.cq · 52.35.Fp