Non-transversal diffusion seems similar to the Arnold diffusion, but it is a different phenomenon since it could be applied to integrable systems in contrast to the Arnold diffusion, which is a phenomenon that only takes place in non integrable systems. In this paper, the existence of the non-transversal heteroclinic chain in the quintic nonlinear Schr?dinger equation is studied. Based on a finite dimensional system of ordinary differential equations, the Toy model system associated with the quintic nonline...
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