Abundant Exact Travelling Wave Solutions for a Fractional Massive Thirring Model Using Extended Jacobi Elliptic Function Method

Abstract

The fractional massive Thirring model is a coupled system of nonlinear PDEs emerging in the study of the complex ultrashort pulse propagation analysis of nonlinear wave functions. This article considers the NFMT model in terms of a modified Riemann–Liouville fractional derivative. The novel travelling wave solutions of the considered model are investigated by employing an effective analytic approach based on a complex fractional transformation and Jacobi elliptic functions. The extended Jacobi elliptic function method is a systematic tool for restoring many of the well-known results of complex fractional systems by identifying suitable options for arbitrary elliptic functions. To understand the physical characteristics of NFMT, the 3D graphical representations of the obtained propagation wave solutions for some free physical parameters are randomly drawn for a different order of the fractional derivatives. The results indicate that the proposed method is reliable, simple, and powerful enough to handle more complicated nonlinear fractional partial differential equations in quantum mechanics.

Solitonic solutions and stability analysis of Benjamin Bona Mahony Burger equation using two versatile techniques

“…Hence, several techniques for solving nonlinear partial differential equations have been developed over the past half-century by a wide range of scientists. such as the simple equation approach 1 – 4 , -expansion method 5 – 7 , modified expansion method 8 , 9 , extended Jacobi elliptic function method 10 , 11 , -expansion method 3 , 12 , 13 , extended -expansion method 14 , Ricati-Bernoulli Sub-ODE method 15 , 16 , extended -function method 17 – 21 and many more 22 – 32 .…”

Sharp Bounds of the Fekete–Szegö Problem and Second Hankel Determinant for Certain Bi-Univalent Functions Defined by a Novel q-Differential Operator Associated with q-Limaçon Domain

“…Due to its numerous uses in mathematical analysis and the physical sciences, such as q-difference operators, fractional and q-symmetric fractional q-calculus, optimal control, qsymmetric functions, and q-integral equations, the q-derivative has undergone accelerated development in a variety of scientific fields in recent decades (for more details, see [1][2][3][4][5][6][7][8]). Jackson introduces the q-difference operator and describes several applications of the qintegral and q-derivative in [9] (see also [10]).…”

Analytical wave solutions of an electronically and biologically important model via two efficient schemes

“…Many different methods have been developed to gain analytical wave solutions of these NLPDEs, i.e., optical soliton solutions of coupled nonlinear Schrödinger equations have been gained with use of Kudryashov R-function technique, [1] some new kinds of optical soliton solutions of time-fractional perturbed nonlinear Schrödinger equations have been achieved by using the generalized Kudryashov scheme, [2] by applying the modified auxiliary equation technique, optical wave solutions of timefractional resonant nonlinear Schrödinger equations have been obtained, [3] new optical wave solutions for the time-fractional perturbed nonlinear Schrödinger equations have been achieved by utilizing the improved tan[φ (ζ /2)]-expansion scheme, [4] different kinds of optical wave solitons of time-fractional paraxial wave equations have been gained by using the Sardar sub-equation method, [5] various optical wave solutions of three-component coupled nonlinear Schrödinger equations have been attained with the help of generalized exponential rational function scheme, [6] dark, bright, singular and periodic solitary wave solutions of generalized fractional Davey-Stewartson equations have been obtained by applying the generalized projective Riccati equation technique, [7] some exact wave solutions of the Lax equation have been achieved by applying the extended sinh-Gordon expansion technique, [8] kink solitons of the Sharma-Tasso-Olver-Burgers equation have been attained by using Kudryashov and exponential techniques, [9] traveling wave solutions of perturbed Biswas-Milovic equations have been gained with the use of improved F-expansion technique, [10] some new optical wave solutions of complex Korteweg-de Vries equations have been obtained by applying the unified scheme. [11] Similarly, Hirota bilinear method, [12] modified extended tanh expansion method, [13] modified simplest equation technique, [14] extended Jacobi elliptic function scheme, [15] sech and tanh function solutions are obtained by using the sine-Gordon expansion scheme, [16] sinh, cosh, sin and cos involving solutions are gained by utilizing the rational sine-Gordon expansion technique [17] and many other techniques. [18][19][20][21][22][23][24] In this study, we use two schemes, i.e., the exp a function and extended sinh-Gordon equation expansion (EShGEE) schemes.…”