New explicit exact solutions of the unstable nonlinear Schrödinger’s equation using the exp a and hyperbolic function methods

High-Order Dispersive Cubic-Quintic Schrödinger Equation and Its Exact Solutions

“…The countless applications of nonlinear evolution equations (NLEEs) in diverse scientific fields have attracted the attention of many academic scholars to search and analyze their exact solutions. In this respect, various methods such as the Kudryashov method [1][2][3][4][5][6][7], tanh-coth method [8,9], modified simple equation method [10,11], sine-cosine method [12,13], transformed rational function method [14,15], ansatz method [16,17], auxiliary equation method [18,19], semi-inverse variational method [20,21], and exp a -function method [22][23][24] have been utilized to solve and handle the NLEEs.…”

A Variety of Explicit Exact and Soliton Type Solutions of Conformable Fractional Equal-Width Equations

“…2 )-expansion methods and the exp function approach have been explored for discrete and fractional order PDEs as well. In particular, Ali and Hassan, Hosseini et al, Zayed and Al-Nowehy all have utilized the exp a function method in [37][38][39][40] respectively. Furthermore, the hyperbolic function approach has been explored in [39,41,42] to procure exact solutions of nonlinear PDEs.…”

“…In particular, Ali and Hassan, Hosseini et al, Zayed and Al-Nowehy all have utilized the exp a function method in [37][38][39][40] respectively. Furthermore, the hyperbolic function approach has been explored in [39,41,42] to procure exact solutions of nonlinear PDEs. This paper aims to explore the hyperbolic function approach to generate new explicit soliton type solutions for the space-time FEW equations [13,14,43] defined with conformable derivative and using the compatible traveling wave transformation.…”

Regarding Rational Exponential and Hyperbolic Functions Solutions of Conformable Time-Fractional Phi-four Equation

“…In particular, Ali and Hassan, Hosseini et al, Zayed and Al-Nowehy all have utilized the exp a function method in [29], [30], [31] and [32] respectively. The hyperbolic function method is one of the most useful approach to procure exact solutions of nonlinear partial differential equations, for example one can study, Xie et al [33], Bai [34] and Hosseini et al [35]. The study of fractional calculus has been given in [36][37][38][39].…”

“…here m and δ are reals. We employ the exp a function approach [29,30,32] and the hyperbolic function approach [33][34][35] via traveling wave transformation with the conformable derivative. The scheme of this paper is as follows: Section 2 presents a brief description of the exp a and the hyperbolic functions methods.…”