Lump, multi-lump, cross kinky-lump and manifold periodic-soliton solutions for the (2+1)-D Calogero-Bogoyavlenskii-Schiff equation.

A bilinear form of the (2+1)-dimensional nonlinear Calogero-Bogoyavlenskii-Schiff (CBS) model is derived using a transformation of dependent variable, which contain a controlling parameter. This parameter can control the direction, wave height and angle of the traveling wave. Based on the Hirota bilinear form and ansatz functions, we build many types of novel structures and manifold periodic-soliton solutions to the CBS model.

Multiple and exact soliton solutions of the perturbed Korteweg-de Vries equation of long surface waves in a convective fluid via Painlevé analysis, factorization, and simplest equation methods.

In this research, the surface waves of a horizontal fluid layer open to air under gravity field and vertical temperature gradient effects are studied. The governing equations of this model are reformulated and converted to a nonlinear evolution equation, the perturbed Korteweg-de Vries (pKdV) equation. We investigate the latter equation, which includes dispersion, diffusion, and instability effects, in order to examine the evolution of long surface waves in a convective fluid.

A new numerical approach to solve Thomas-Fermi model of an atom using bio-inspired heuristics integrated with sequential quadratic programming.

In this study, a novel bio-inspired computing approach is developed to analyze the dynamics of nonlinear singular Thomas-Fermi equation (TFE) arising in potential and charge density models of an atom by exploiting the strength of finite difference scheme (FDS) for discretization and optimization through genetic algorithms (GAs) hybrid with sequential quadratic programming. The FDS procedures are used to transform the TFE differential equations into a system of nonlinear equations. A fitness function is constructed based on the residual error of constituent equations in the mean square sense and is formulated as the minimization problem.