Analysis of chaotic structures, bifurcation and soliton solutions to fractional Boussinesq model

Abstract

In this work, we used the space-time fractional coupled Boussinesq (STFCB) model that is essential tools in the study of quantum optics, steady physics, the variational string's acoustic waves, ion vibrational frequencies, hydro-magnetic waves in cold plasma and many other fields.~In order to put such new precise solutions of the aforementioned model, the modified Sardar-sub equation (MSSE) technique has been suggested with inside the sense of conformable derivative and the fractional order partial differential equation that is capable of changing into an ordinary differential equation by using the travelling wave transform.~The scoring of solitons and other solutions demonstrates the MSSE technique compatibility for different constant values, which are shown in 3-D, 2-D and contour plots.~Additionally, we discussed the examined model chaotic and dynamical tendencies.~The theory of plane dynamical system is used to examine the chaotic patterns of the systems.~The investigations are novel and unexamined.~They can be utilized to explain the physical phenomena which have been simulated to provide details on the brief dynamical characteristics.~According to numerical simulations modifying the parameters of frequencies and amplitudes has an impact on the system of dynamical properties. We indicated that the MSSE technique for creating precise solutions offers new and significant mathematical tools in applied mathematics.

Dynamical behavior of chaos, bifurcation analysis and soliton solutions to a Konno-Onno model

“…Derivate Eq (14), twice with the help of considering Eq (9), to get a polynomial in the power of K(C). Collect all the coefficients which have the same powers of the K(C) and after that, set each coefficient to zero.…”

“…In order to solve FPDEs analytically, a variety of analytical techniques were developed, including the modified -expansion technique [ 10 , 11 ], the Hirota bilinear technique [ 12 ], the kather technique [ 13 ], the modified Sardar sub-equation technique [ 14 ], the expansion method [ 15 ], the direct algebraic technique [ 16 ] and many others [ 17 – 20 ].…”

Taking into consideration a fifth-order nonlinear Schrödinger equation in an optical fiber

“…Nonlinear studies in oceanography, acoustics, finance, fluid mechanics and nonlinear optics have been productive [1][2][3][4][5][6][7][8]. The propagation of the picosecond pulses in an optical fiber can be described by the following nonlinear Schrödinger equation:…”

Fractional Fokas-Lenells equation: analyzing travelling waves via advanced analytical method

“…In particular, the NPSE and YTSF equation have been analyzed regarding optical fibers and engineering [37,38]. In turn, the 2D-SCNLSE [39] has been solved stochastically and the STFCB model involved in quantum optics and physics [40]. Moreover, generalized fractional calculus operators have recently received more attention and the corresponding incomplete ℵ-functions are nowadays more refined [41].…”