In the present paper, we are concerned with the link between the Kadomtsev–Petviashvili–Toda (KP–Toda) hierarchy and the massive Thirring (MT) model. First, we bilinearize the MT model under both the vanishing and nonvanishing boundary conditions. Starting from a set of bilinear equations of two‐component KP–Toda hierarchy, we derive multibright solution to the MT model. Then, considering a set of bilinear equations of the single‐component KP–Toda hierarchy, multidark soliton and multibreather solutions to the MT model are constructed by imposing constraints on the parameters in two types of tau function, respectively. The dynamics and properties of one‐ and two‐soliton for bright, dark soliton and breather solutions are analyzed in details.
 Award ID(s):
 1715991
 NSFPAR ID:
 10374275
 Date Published:
 Journal Name:
 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
 Volume:
 478
 Issue:
 2258
 ISSN:
 13645021
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract 
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