Localized waves for a complex nonisospectral nonpotential sine-Gordon equation

Abstract The nonisospectral effect λ t = α ( t ) λ satisfied by spectral parameter λ opens up a new scheme for constructing localized waves to some nonlinear partial differential equations. In this paper, we perform this effect on a complex nonisospectral nonpotential sine-Gordon equation by the bilinearization reduction method. From an integrable nonisospectral Ablowitz–Kaup–Newell–Segur equation, we construct some exact solutions in double Wronskian form to the reduced complex nonisospectral nonpotential sine-Gordon equation. These solutions, including soliton solutions, Jordan-block solutions and interaction solutions, exhibit localized structure, whose dynamics are analyzed with graphical illustration. The research ideas and methods in this paper can be generalized to other negative order nonisospectral integrable systems.