Abstract
The non-integrable behavior in one-dimensional generalized nonlinear Schrödinger equations involving high order saturable nonlinearities, which govern the dynamic behavior in a class of physical systems, is investigated numerically. The numerical results illustrate that the high order saturable nonlinearities would lead to chaos, where the irregular homoclinic orbit (HMO) crossings have been observed in phase space. On the other hand, we show that the periodic solutions and solitary waves may exist in such non-integrable continuum Hamiltonian dynamic systems.
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