The traditional (G/G2 ) expansion method is modified to extend the symmetric extension to the negative power term in the solution to the positive power term. The general traveling wave solution is extended to a generalized solution that can separate variables. By using this method, the solution to the detached variables of the symmetric extended form of the 2+1-dimensional NNV equation can be solved, also the soliton structure and fractal structure of Dromion can be studied well.
In order to analyze the motion characteristics of spring pendulum under the action of magnetic force, the motion of spring pendulum after applying a uniform magnetic field in a straight direction is considered. The first order approximate solution is given by studying the micro-vibration near the equilibrium point. The approximate solutions similar to Foucault's pendulum are also obtained considering the large weight of the pendulum ball and the soft spring. Then, a new internal resonance phenomenon of magnetic spring pendulum is found by harmonic balance method, and the conclusion is that the energy is transmitted in three modes of respiration, swing and deflection in sequence.Finally, the influence of magnetic field on the stability of spring pendulum is investigated, and the bifurcation phenomenon at its equilibrium point is found.
The N-soliton solution of the (2+1)-dimensional Sawada-Kotera equation is given by using the Hirota bilinear method, and then, the conjugate parameter method and the long-wave limit method are used to get the breather solution and the lump solution, as well as the interaction solution of the elastic collision properties between them. In addition, according to the expression of the lump-type soliton solution and the striped soliton solution, the completely inelastic collision, rebound, absorption, splitting, and other particle characteristics of the two solitons in the interaction process are directly studied with the simulation method, which reveals the laws of physics reflected behind the phenomenon.
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