ADM-Padé technique for the nonlinear lattice equations

Traveling Wave Solutions for Nonlinear Differential-Difference Equations of Rational Types

“…to zero, we obtain a system of nonlinear algebraic equations from which the unspecified constants a i , d i , c j and µ can be explicitly found. Finally, substituting these results into (17) will lead to varies kind of traveling wave solutions for (14).…”

“…As a result, quite a few new modifications of the existing methods for dealing with NEEs has been put forth to solve nonlinear DDEs. The most commonly used ones are Hirota's bilinear method, [8] Jacobi elliptic function expansion method, [9] Tau method, [10] extended Jacobian elliptic function algorithm, [11] Exp-function method, [12] Riccati equation expansion method, [13] ADMPadé technique, [14] homotopy perturbation method, [15] discrete tanh method, [16] and so on.…”

The discrete (G′/G)‐expansion method applied to the differential‐difference Burgers equation and the relativistic Toda lattice system

“…Zhen [11] devised a discrete hyperbolic tangent method for solving NDDEs. Yang et al [12] investigated two nonlinear lattice equations via the so-called ADM-Padé technique. Aslan [13] demonstrated the applicability of the extended simplest equation method to NDDEs, etc.…”

Discrete exact solutions to some nonlinear differential-difference equations via the (G′/G)-expansion method

“…Zhu [29,30] extended the Exp-function method to NDDEs to obtain physically important solutions. Yang et al [31] considered two nonlinear lattice equations using the so-called ADM-Padé technique. The homotopy perturbation method is applied by Zhu et al [32] to a nonlinear differential-difference equation arising in nanotechnology.…”