2018 **Abstract:** We apply the ( / 2 )-expansion method to construct exact solutions of three interesting problems in physics and nanobiosciences which are modeled by nonlinear partial differential equations (NPDEs). The problems to which we want to obtain exact solutions consist of the Benny-Luke equation, the equation of nanoionic currents along microtubules, and the generalized Hirota-Satsuma coupled KdV system. The obtained exact solutions of the problems via using the method are categorized into three types including trigo…

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“…where a = 0, b, c, λ(< 0), µ, k are arbitrary constants. From Equations (10), (20), and 22, we obtain the traveling wave solution of Equation 1as follows:…”

confidence: 99%

“…where a = 0, b, c, λ(< 0), µ, k are arbitrary constants. From Equations (10), (20), and 22, we obtain the traveling wave solution of Equation 1as follows:…”

confidence: 99%

“…where a 0 , a = 0, b, c, λ(> 0), µ are arbitrary constants and σ 2 = A 2 1 + A 2 2 , where A 1 , A 2 are arbitrary constants. From Equations (12), (20), and (29), we obtain the exact solution of Equation (1) as follows:…”

confidence: 99%

“…With the development of solution theory, many powerful methods for obtaining the exact solutions of NLEEs have been presented by many authors. For instances, Tanh method [2,3], F-expansion method [4], Backlund transforms [5], a numerical simulation and explicit solutions [6], Adomian decomposition method (ADM) [3,9], variational iteration method [3,12], the Jacobi elliptic function expansion method [13], ( ′ / , 1/ ) -expansion method [15], inverse scattering transform [20], Modified Pseudospectral method [21], spectral collocation method [22], an efficient algorithm method [24], finite element analysis and numerical method [25], ( ′ / 2 )expansion method [26], Exp-function method [28].…”

confidence: 99%