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We analytically investigate transverse magnetic (TM) spatial bright solitons,as exact solutions of Maxwell's equations, propagating through nonlinearmetamaterials whose linear dielectric permittivity is very close to zero andwhose effective nonlinear Kerr parameters can be tailored to achieve values notavailable in standard materials. Exploiting the fact that, in the consideredmedium, linear and nonlinear polarization can be comparable at feasible andrealistic optical intensities, we identify two novel self-trapping mechanismsable to support two-peaked and flat-top solitons, respectively. Specifically,these two novel mechanisms are based on the occurrence of critical points atwhich the effective nonlinear permittivity vanishes, the two mechanismsdiffering in the way the compensation between linear and nonlinear polarizationis achieved through the non-standard values of the nonlinear parameters.

Two-peaked and flat-top perfect bright solitons in epsilon-near-zero nonlinear metamaterials: novel Kerr self-trapping mechanisms