keywords: Applications of Nonlinear Sciences; Applications in Engineering and Nanoscience.In recent decades the III-Nitrides semiconductors (like Gallium Nitride, Aluminium Nitride, and Indium Nitride) have been the object of intensive study. This is a consequence of the realization of the long-awaited possibility of growing satisfactory samples, leading to the increased development of electronic and opto-electronic devices (blue diodes, blue lasers, etc.) of large technological and industrial interest [1,2,3]. The GaN and AlN are semiconductors with band gaps and other characteristics that largely differ from those of InN (it may be noticed that it resembles the case of InAs in the family of the III-V semiconductors). Recently, the band gap of InN has been clarified as being 0.64 eV [4][5][6][7][8], which corresponds to the near infra-red region and enables AlN-GaN-InN-based nitride materials to be used for fabricating devices operating from the UV to near infra-red range. These properties of nitride semiconductors are being used to develop high efficiency tandem-type solar cells.Further, InN can be readily made as the n-type by introducing crystal defects [3]. Of large relevance are the studies of their optical and transport properties in situations in which they are working in far-fromequilibrium conditions. When under the action of intermediate to strong electric fields their transport properties are nonlinear (in the electric field intensity).We have considered such question in a series of papers (e.g. Refs. [9-10]), and in the present paper we are adding a study on the coupled influence of the electric field strength and the concentration of carriers on the nonlinear mobility (that is, a mobility dependent nonlinearly on field and concentration) in n-doped InN.In the study of transport phenomena it has been used variations of computational modeling approaches (in the domain of Nonequilibrium Molecular Dynamics and related to Monte Carlo computational methods). On the other hand, improved analytical methods, that is, nonlinear quantum kinetic theories for studying physical phenomena in systems arbitrarily departed from equilibrium, are desirable. An advantage that they may present in relation to the computational-modeling methods resides in that the explicit equation of motion for the basic nonequilibrium thermodynamic variables, which characterize the dissipative macrostate of the system, provide a better physical insight and interpretation of the results.Nonequilibrium quantum kinetic theories based on various intuitive techniques and ideas are presently available. One particularly appropriate for the purpose just stated, and which offers an elegant and concise analytical treatment of the theory of irreversible processes, has been derived from an approach based on a nonequilibrium ensemble formalism (since it can be founded on a variational principle, consisting in the maximization of the informational entropy in the statistical description, for short it is referred to as MaxEnt-NESOM [17][18][19][20][21]...