“…Equation (1) can be easily solved by a numerical method (Li and He, 2019; Alizadeh et al , 2018; Liu, 2019; Pirmohammadi, 2019; Bilige and Han, 2018), and it can be solved by many analytical methods, for example, the variational method, the variational iteration method (He and Latifizadeh, 2020; Anjum and He, 2019; He et al , 2014), the homotopy perturbation method (Yu et al , 2019; Ren et al , 2019; Ban and Cui, 2018; Wu and He, 2018) and Taylor series method (He and Ji, 2019b; He et al , 2019; He, 2019a; Khan, 2018). In this paper, we will apply the exp-function method (He, 2012; He, 2013; He and Wu, 2006; Jia et al , 2015) to study the solution properties at different scales.…”