Exact soliton of (2 + 1)-dimensional fractional Schrödinger equation

A novel analytical technique to obtain the solitary solutions for nonlinear evolution equation of fractional order

“…Several authors have been discussed the simplified modified Camassa-Holm (SMCH) equation by using different techniques for finding exact traveling wave results. Particularly, Liu et al [22] used the (G /G)-expansion method, Najafi et al [23], used He's semi-inverse method applied exp(-ϕ(η))-expansion method and Redi et al [19] applied an improved (G /G)-expansion method; Gundogdu et al [28] applied the elliptic function expansion method to get the traveling wave solutions. Akber et al [26] obtained solutions u 1 (φ), u 3 (φ), u 6 (φ), u 7 (φ) and u 8 (φ) that are equivalent to our solutions u 10 (η), u 19 (η) and u 20 (η).…”

“…Fractional calculus is a dominant tool in several nonlinear fields such as plasma physics, fluid mechanics, solid-state physics, optical fibers, quantum field theory, biophysics, chemical kinematics, electricity, chemistry, biology, geochemistry, propagation of shallow water waves and engineering [7,10,16]. For this purpose many techniques were used such as the homogeneous balance method [17], the exp-function method [18], the improved extended F-expansion method [19], and the homotopy perturbation method [20]. The Camassa-Holm (CH) equation is…”

New Travelling Wave Solutions for KdV6 Equation Using Sub Equation Method

“…In the last years, the number of studies on fractional partial differential equations have increased since they can be used in many fields such as physics, engineering, biology and chemistry [1][2][3]. Most of these studies focused on obtaining the exact solutions of fractional partial differential equations [13,14]. But, some of the fractional derivative definitions such as Riemann-Liouville and Caputo do not have capabilities to achieve the exact solutions.…”

Rogue Wave Solutions and Modulation Instability With Variable Coefficient and Harmonic Potential

“…These waves are also found in deep and shallow water and, beyond oceanic expanses, in optical fibers [1][2][3][4][5][6][7][8], super fluids, and so on [9][10][11][12][13][14][15][16][17][18]. In recent times, the theoretical study of these kinds of waves has become an interesting part of the field of nonlinear sciences [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. The following section deals with the extraction of wave solutions with ST.…”