Solitary wave solutions and sensitivity analysis to the space-time β-fractional Pochhammer-Chree equation in elastic medium.

Solitary wave solutions to the nonlinear evolution equations have recently attracted widespread interest in engineering and physical sciences. In this work, we investigate the fractional generalised nonlinear Pochhammer-Chree equation under the power-law of nonlinearity with order m. This equation is used to describe longitudinal deformation wave propagation in an elastic rod.

On the study of solitary wave dynamics and interaction phenomena in the ultrasound imaging modelled by the fractional nonlinear system.

This research work focuses on investigating the propagation of ultrasonic waves, which propagate mechanical vibrations of molecules or particles inside materials. Ultrasound imaging is extensively used and deeply rooted in the medical field. The key technologies that form the basis for many different uses in the area include transducers, contrast agents, pulse compression, beam shaping, tissue harmonic imaging, techniques for measuring blood flow and tissue motion, and three-dimensional imaging.

Analysis of fractional solitary wave propagation with parametric effects and qualitative analysis of the modified Korteweg-de Vries-Kadomtsev-Petviashvili equation.

This study explores the fractional form of modified Korteweg-de Vries-Kadomtsev-Petviashvili equation. This equation offers the physical description of how waves propagate and explains how nonlinearity and dispersion may lead to complex and fascinating wave phenomena arising in the diversity of fields like optical fibers, fluid dynamics, plasma waves, and shallow water waves. A variety of solutions in different shapes like bright, dark, singular, and combo solitary wave solutions have been extracted.

Propagation of the pure-cubic optical solitons and stability analysis in the absence of chromatic dispersion.

The main concentration of this article is to extract pure-cubic optical solitons in nonlinear optical fiber modeled by nonlinear Schrödinger equation (NLSE). The governing model is discussed the with the effect of third-order dispersion, Kerr law of nonlinearity and without chromatic dispersion. We extract the solutions in different forms like, Jacobi's elliptic, hyperbolic, periodic, exponential function solutions including a class of solitary wave solutions such that bright, dark, singular, kink-shape, multiple-optical soliton, and mixed complex soliton solutions.