Bilinear Bäcklund transformation, kink soliton, nonsingular complexiton and singular complexiton wave solutions to the (3+1)-dimensional Jimbo–Miwa equation

This work focuses on exploring the Bilinear Bäcklund transformation (BT) and several novel exact wave solutions for the (3[Formula: see text]1)-dimensional Jimbo–Miwa equation (JME) in the fields of optics, quantum field theory, fluid mechanics, plasma physics, etc. Utilizing the Hirota Bilinear form (HBF) derived through the Cole–Hopf transformation, we develop the Bilinear BT consisting of four equations with four free parameters. Then, the corresponding kink soliton solution is also obtained based on the BT. In addition, two different complexiton solutions, such as the singular complexiton (SC) and nonsingular complexiton (NSC) solutions, are derived by bringing the conjugate constraint conditions into the resonant multiple wave solutions, which are attained by the linear superposition method (LSM) and weight algorithm (WA). The wave structures of these exact soliton solutions are illustrated to reveal their physical attributes by selecting the appropriate parameter values.