The properties of microscopic particles depicted by quantum mechanics in linear systems and the difficulties and problems of quantum mechanics are first debated, the reasons resulting in these difficulties and direction of development of quantum mechanics are studied in detail. From this study, we know the essence of linearity of quantum mechanics, which needs to develop further forward. In such a case, we propose using the nonlinear Schrödinger equation to describe the microscopic particles in nonlinear quantum systems including condensed matters. Thus, we investigate completely and deeply the natures and features of microscopic particles described by nonlinear Schrödinger equation, especially their wave-corpuscle features and rules of motion. Concretely speaking, we investigate in this paper, the wave-particle duality of the solution of the nonlinear Schrödinger equation, the stability of microscopic particles described by nonlinear quantum mechanics, invariances and conservation laws of motion of particles, the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamiltonian equations, the classical rule of microscopic particle motion, the mechanism and rules of particle collision, the features of reflection and the transmission of particles at interfaces, and the uncertainty relation of particle’s momentum and position. We obtain the invariance and conservation laws of mass, energy and momentum and angular momentum for the microscopic particles, which are also some elementary and universal laws of matter in nonlinear quantum mechanics. We also find that the laws of motion of microscopic particles described by the new theory are completely different from that in the linear quantum mechanics. They have a lot of new properties; for example, the particles possess the wave-corpuscle duality, obey the classical rule of motion and conservation laws of energy, momentum and mass, satisfy minimum uncertainty relation, can be localized due to the nonlinear interaction, and its position and momentum can also be determined at a certain degree, etc. From these studies, we see clearly that rules and features of microscopic particle motion depicted by nonlinear Schrödinger equation in nonlinear quantum systems containing condensed matters are different from those described by linear Schrödinger equation in linear quantum mechanics, the latter is a special case of the former at the nonlinear interaction equal to zero. The nonlinear quantum theory is a new physical theory, and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear quantum systems, which can solve difficulties and problems disputed for about a century by scientists in the linear quantum mechanics field. Hence, it is very necessary to build nonlinear quantum mechanics, which can promote the development of physics including condensed matter physics, and can enhance and raise the knowledge and recognition levels to the essences of microscopic matter.