This text introduces readers to the algebraic concepts of group and rings, providing a comprehensive discussion of theory as well as a significant number of applications for each. Number Theory: Induction; Binomial Coefficients; Greatest Common Divi
We consider the application of Koopman theory to nonlinear partial differential equations. We demonstrate that the observables chosen for constructing the Koopman operator are critical for en- abling an accurate approximation to the nonlinear dynami
We present the numerical results of both head-on and non-head-on collisions between two stable dissipative optical bullets (DOBs) in a three-dimensional complex Ginzburg-Landau equation with cubic-quintic nonlinearity. The system parameters chosen ar
The synthetic effects of group-velocity mismatch and cubic-quintic nonlinearity on cross-phase modulation induced modulation instability in loss single-mode optical fibers have been numerically investigated. The results show that the quintic nonlinea
In this work, new plain and composite high-energy solitons of the cubic–quintic Swift–Hohenberg equation were numerically found. Starting from a composite pulse found by Soto-Crespo and Akhmediev and changing some parameter values allowed us to find
