Abstract
A (2+1)-dimensional coupled nonlocal nonlinear Schrodinger equation is studied in \({\mathcal {PT}}\)-symmetric nonlocal nonlinear couplers with gain and loss, and approximate self-similar solution of vector rotating azimuthon is obtained. Various structures of rotating azimuthon and soliton cluster are constructed. Moreover, dynamical behaviors of azimuthon and soliton cluster are discussed in the constant diffraction system and the exponential diffraction decreasing waveguide.
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