An improved base-f expansion method is proposed, in which the bit-length of coefficients is shorter and the number of coefficients is smaller than in Kobayashi’s expansion method. The proposed method meshes well with efficient multi-exponentiation algorithms. In addition, two efficient algorithms based on the proposed expansion method, named f-wNAF and f-SJSF, are presented which significantly ...

G 󸀠 /G-expansion method which is employed to investigate the solitary and periodic traveling waves of this equation. As a result, some new traveling wave solutions involving hyperbolic functions, the trigonometric functions, are obtained.When the parameters are taken as special values, the solitary wave solutions are derived from the hyperbolic function solutions, and the periodic wave solution...

Further extension of the generalized and improved (G0/G)-expansion method; Nonlinear ordinary differential equation; ZKBBM equation; Travelling wave solutions Abstract In this article, the generalized and improved (G0/G)-expansion method has been proposed for further extension to generate many new travelling wave solutions. In addition, nonlinear ordinary differential equation is implemented as...

A generalized and improved G′/G -expansion method is proposed for finding more general type and new travelling wave solutions of nonlinear evolution equations. To illustrate the novelty and advantage of the proposed method, we solve the KdV equation, the Zakharov-KuznetsovBenjamin-Bona-Mahony ZKBBM equation and the strain wave equation in microstructured solids. Abundant exact travelling wave s...

The generalized and improved (G'/G)-expansion method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. In this article, we investigate the higher dimensional nonlinear evolution equation, namely, the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation via this powerful method. The solutions...

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To ver...

we apply the improved G′/G -expansion method for constructing abundant new exact traveling wave solutions of the 2 1 -dimensional Modified Zakharov-Kuznetsov equation. In addition, G ′′ λG′ μG 0 together with b α ∑w q −w pq G ′/G q is employed in this method, where pq q 0,±1,±2, . . . ,±w , λ and μ are constants. Moreover, the obtained solutions including solitons and periodic solutions are des...