  In linear communication channels, spectral components (modes) defined by the
Fourier transform of the signal propagate without interactions with each other.
In certain nonlinear channels, such as the one modelled by the classical
nonlinear Schr\"odinger equation, there are nonlinear modes (nonlinear signal
spectrum) that also propagate without interacting with each other and without
corresponding nonlinear cross talk; effectively, in a linear manner. Here, we
describe in a constructive way how to introduce such nonlinear modes for a
given input signal. We investigate the performance of the nonlinear inverse
synthesis (NIS) method, in which the information is encoded directly onto the
continuous part of the nonlinear signal spectrum. This transmission technique,
combined with the appropriate distributed Raman amplification, can provide an
effective eigenvalue division multiplexing with high spectral efficiency,
thanks to highly suppressed channel cross talk. The proposed NIS approach can
be integrated with any modulation formats. Here, we demonstrate numerically the
feasibility of merging the NIS technique in a burst mode with high spectral
efficiency methods, such as orthogonal frequency division multiplexing and
Nyquist pulse shaping with advanced modulation formats (e.g., QPSK, 16QAM, and
64QAM), showing a performance improvement up to 4.5 dB, which is comparable to
results achievable with multi-step per span digital back propagation.
