We solve the higher order nonlinear Schrödinger equation describing the propagation of ultrashort pulses in optical fibers. By means of the coupled amplitude-phase formulation fundamental (solitary wave) dark soliton solutions are found.

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High-temperature magnetization and neutron diffraction measurements on metastable Fe x Cu 100−x solid solutions have recently shown to imply that ␥-Fe precipitates present ferromagnetic anti-Invar behavior. For this reason, we have studied the ferromagnetic phases of ␥-Fe in moment-volume parameter space, using the general potential linearized-augmented plane-wave method and the fixed spin moment procedure in order to calculate the corresponding total energy. We find that only two ferromagnetic phases ͑one related to a low-spin state and the other to a high-spin state͒ can exist and even coexist in limited volume ranges ͑3.55-3.59 Å͒. Hence, our results provide a "revisited" version of the local spin density calculations used in the early article by Moruzzi et al. ͓Phys. Rev. B 34, 1784 ͑1986͔͒. In addition, the fixed spin moment method-using an energy-moment-volume space representation-allows us to conclude that the high-spin state is the ground state of the ␥-Fe precipitates, as the anti-Invar behavior is an intrinsic property of these states. This simple scenario seems to adequately describe the perplexing phenomenology recently observed on Fe x Cu 100−x solid solutions.