Further Results about Seeking for the Exact Solutions of the Nonlinear 2 + 1 -Dimensional Jaulent-Miodek Equation

Nonlinear science is a great revolution of modern natural science. As a result of its rise, the various branches of subjects characterized by nonlinearity have been developed vigorously. In particular, more attention to acquiring the exact solutions of a wide variety of nonlinear equations has been paid by people. In this paper, three methods for solving the exact solutions of the nonlinear 2 + 1 -dimensional Jaulent-Miodek equation are introduced in detail. First of all, the exact solutions of this nonlinear equation are obtained by using the exp − ϕ z -expansion method, tanh method, and sine-cosine method. Secondly, the relevant results are verified and simulated by using Maple software. Finally, the advantages and disadvantages of the above three methods listed in the paper are analyzed, and the conclusion was drawn by us. These methods are straightforward and concise in very easier ways.

Complexity of a Microblogging Social Network in the Framework of Modern Nonlinear Science

Recent developments in nonlinear science have caused the formation of a new paradigm called the paradigm of complexity. The self-organized criticality theory constitutes the foundation of this paradigm. To estimate the complexity of a microblogging social network, we used one of the conceptual schemes of the paradigm, namely, the system of key signs of complexity of the external manifestations of the system irrespective of its internal structure. Our research revealed all the key signs of complexity of the time series of a number of microposts. We offer a new model of a microblogging social network as a nonlinear random dynamical system with additive noise in three-dimensional phase space. Implementations of this model in the adiabatic approximation possess all the key signs of complexity, making the model a reasonable evolutionary model for a microblogging social network. The use of adiabatic approximation allows us to model a microblogging social network as a nonlinear random dynamical system with multiplicative noise with the power-law in one-dimensional phase space.