Exact solitary solutions of an inhomogeneous modified nonlinear Schrödinger equation with competing nonlinearities

Mechanical Models of Microtubules

“…A common example for Φ is a solution of Riccati equation, which is either tangent or tangent hyperbolic. As only the latter function may have physical meaning, we call the method as tangent hyperbolic function method (THFM) [25,[33][34][35] and extended or modified extended THFM [36]. The function Φ can also be one of Jacobian elliptic functions [37] and, even, unknown [38].…”

He's variational method for a (2 + 1)-dimensional soliton equation

“…It has recently become more interesting to obtain exact solutions of nonlinear partial differential equations (NPDEs) using symbolic computation softwares such as Maple, Mathematica and Matlab that facilitate complex and tedious algebraical computations. In recent years, various effective methods have been developed to find the exact solutions of NPDEs, such as tanh-function method [4,5,6,7,8,9,10,11], generalized hyperbolic function method [12], homogeneous balance method [13,14], Jacobi-elliptic function method [15,16,17], exp-function method [18,19], auxiliary equation method [20,21,22,23,24] and so on, e.g. see [25,26,27].…”

Elastic collision of mobile solitons of a (3 + 1)-dimensional soliton equation

“…Recently, various powerful methods have been utilized to explore different kind of solutions for nonlinear partial differential equations. However, the direct searching for exact solutions of nonlinear evolution equations has become more attractive due to the availability of computer symbolic systems like Maple and Mathematica which allows us to perform some complicated and tedious algebraic calculations on computer, as well as helping us to find new exact solutions of nonlinear evolution equations using the effective methods such as the homogeneous balance method [8,9], tangent hyperbolic function method and modified extended tangent hyperbolic function method [10][11][12][13][14][15][16][17], sine-cosine method [18,19], Jacobi elliptic function method [20][21][22][23], double exponential function method [24], Riccati method [25,26], F-expansion and extended F-expansion methods [27], modified extended homoclinic test approach [28] and other methods [29][30][31][32][33]. From these, many of them are used to solve integral evolution equations for analytical solutions conveniently.…”