Quiescent optical solitons with complex Ginzburg-Landau equation having a dozen forms of self-phase modulation.

The current study focuses on the recovery of quiescent optical solitons through the use of the complex Ginzburg-Landau equation when the chromatic dispersion is rendered to be nonlinear. A dozen forms of self-phase modulation structures are taken into consideration. The utilization of the enhanced Kudryashov's scheme has led to the emergence of singular, dark, and bright soliton solutions.

Dispersive optical solitons and conservation laws of Radhakrishnan-Kundu-Lakshmanan equation with dual-power law nonlinearity.

The current paper implements three elegant approaches to recover a complete spectrum of optical solitons to the Radhakrishnan-Kundu-Lakshmanan equation with dual-power law of nonlinear refractive index. The conservation laws are also recovered by the usage of multipliers approach. The parameter constraints for the existence of such solitons are also enumerated.

Exact traveling wave solutions for system of nonlinear evolution equations.

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics.