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The nonlinear propagation of positron acoustic periodic (PAP) travelling waves in a magnetoplasma composed of dynamic cold positrons,superthermal kappa distributed hot positrons and electrons,and stationary positive ions is examined.The reductive perturbation technique is employed to derive a nonlinear Zakharov-Kuznetsov equation that goves the essential features of nonlinear PAP travelling waves.Moreover,the bifurcation theory is used to investigate the propagation of nonlinear PAP periodic travelling wave solutions.It is found that kappa distributed hot positrons and electrons provide only the possibility of existence of nonlinear compressive PAP travelling waves.It is observed that the superthermality of hot positrons,the concentrations of superthermal electrons and positrons,the positron cyclotron frequency,the direction cosines of wave vector k along the z-axis,and the concentration of ions play pivotal roles in the nonlinear propagation of PAP travelling waves.The present investigation may be used to understand the formation of PAP structures in the space and laboratory plasmas with superthermal hot positrons and electrons.