We report on the triggering of localized and confined chaos described by a general cubic order damped nonlinear Schrödinger amplitude equation containing a conjugate amplitude term, representing the time-periodic parametric driving, and a spatially periodic term representing the external potential that cuts and confines the chaotic patterns promoted by the former, leading to trapped chaotic space-localized structures. Numerical simulations in 1 + 1, 1 + 2, and 1 + 3 dimensions, Lagrangian and Hamiltonian theories for continuous fields, moments method, largest Lyapunov exponents, spectral distributions, and bifurcations diagrams are used to characterize and analyze these chaotic solitons.
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