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Bifurcations and exact solutions of nonlinear Schr\"{o}dinger equation with an anti-cubic nonlinearity
Keywords:Periodic solution, periodic peakon, compacton solution, bifurcation, homoclinic solution, nonlinear Schr\"{o}dinger equation with an anti-cubic nonlinearity.
      the method of dynamical systems, we obtain bifurcations of the phase portraits of the corresponding planar dynamical system under different parameter conditions. Corresponding to different level curves defined by the Hamiltonian, we derive all exact explicit parametric representations of the bounded solutions (including periodic peakon solutions, periodic solutions, homoclinic solutions, heteroclinic solution and compacton solutions).