Point symmetries of the Lie of the complex Ginzburg-Landau equation
Keywords:
Soliton theory, symmetry, nonlinear optics, Gauss potential, Lie algebra.Abstract
A soliton is a nonlinear single moving wave that retains its shape and velocity during its movement, that is, it is a constant formation, and when it collides with isolated waves similar to itself, the phenomenon of a mutual phase shift of two waves occurs, that is, the only result of the interaction of solitons may be some kind of shift in phase.
In this paper, we will study the distribution of the soliton constant in the complex Ginzburg-Landau equation (CGL) with a nonlinear regime that focuses on itself in the presence of a symmetric Gaussian potential. For many decades, nonlinear systems have attracted researchers theoretically and experimentally with their rich dynamic characteristics. Such nonlinear systems can be conservative (closed) or dissipative (open), and both support solitons. A soliton is nothing but a constant profile of light pulses in an optical system. In the case of a dissipative nonlinear system, in addition to dispersion and nonlinear equilibrium, it is possible to continuously propagate a light pulse or soliton to achieve a balance between dissipation (loss) and gain. This means that a dissipative system cannot support continuous families of solitons similar to conservative systems. In other words, in a dissipative system, the distribution of solitons can be determined by the parameters of the system, while in a conservative system it is determined by the input optical pulse. This increases the experimental feasibility of determining the area of a stable soliton in a dissipative system by simply manipulating the system.
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