New solitary wave solutions for the conformable Klein-Gordon equation with quantic nonlinearity

Abundant exact solutions to a generalized nonlinear Schrödinger equation with local fractional derivative

“…The generalized nonlinear Schrödinger dynamic equation (NLSE) with group velocity dispersion and second‐order spatiotemporal dispersion coefficients is an important mathematical model that illustrates the dynamics of optical soliton promulgation in the optical fibers for trans‐continental 23,24 . During the past years, a wide variety of analytic and numeric methods have been developed to integrate partial differential equations arising in various physical aspects of applied sciences 25–36 …”

Solitary and Rogue Wave Solutions to the Conformable Time Fractional Modified Kawahara Equation in Mathematical Physics

“…Frequent investigators arranged through nonlinear evolution equations (NEEs) to form voyaging wave arrangement by executing a few arrangements. The approaches that are engrained in continuing writing are as follows: the double subequation approach [4], multiple exp-function algorithm [5], improved subequation scheme [6,7], modified simple equation technique [8], tanh-coth scheme [9], sine-cosine strategy [10], first integral approach [11], ðG′/G, 1/GÞ -expansion scheme [12], fractional reduced differential trans-form method [13], extended Kudryashov scheme [14], modified simple equation scheme [15], new extended (G ′ /G) expansion scheme [16,17], functional variable method [18], trial solution scheme [19], scheme exp-function approach [20], multiple simplest equation scheme [21], exp ð−ϕðξÞÞ -expansion scheme [22][23][24][25][26], pseudoparabolic model [27][28][29], sine-Gordon expansion scheme [30], modified extended tanh-function scheme [31], modified auxiliary expansion scheme [32], method of line [33], Bernoulli subequation function technique [34,35], modified exponential function scheme [36], improved Bernoulli subequation function scheme [37], and the finite difference scheme [38].…”

Soliton solutions of nonlinear fractional differential equations with its applications in mathematical physics

“…New exact solutions might be used to find new phenomena in this field. In the literature, there are many methods to find new exact solutions, such as the tanh-sech method [1], the functional variable method [2][3][4], the expfunction method [5,6],(G'/G)-expansion method [7,8], the generalized exponential rational function method [9][10][11], the reproducing kernel method [12], Hirota method [13,14] and the ansatz method [15,16].…”