A multiple exp-function method for nonlinear differential equations and its application

By Wenxiu Ma, Tingwen Huang, Yi Zhang. 2010

659 citations recorded by the source corpus.

A multiple exp-function method for exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards the ease of use and capability of computer algebra systems and provides a direct and systematic solution procedure that generalizes Hirota's perturbation scheme. With the help of Maple, applying the approach to the (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama equation yields exact explicit one-wave, two-wave and three-wave solutions, which include one-soliton, two-soliton and three-soliton type solutions. Two cases with specific values of the involved parameters are plotted for each of the two-wave and three-wave solutions.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/aede632b1caae8574a3661d459519ad550d36f3c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Zuo-nong Zhu
2. M. Akbar
3. Abdul-Ghani A. A. H. Al-Nowehy
4. Elsayed M. E. Zayed
5. Kamruzzaman Khan
6. Wenxiu Ma

In Statistical and Nonlinear Physics

1. M. Akbar
2. Kamruzzaman Khan
3. Zuo-nong Zhu
4. Wenxiu Ma
5. Elsayed M. E. Zayed
6. Abdul-Ghani A. A. H. Al-Nowehy
7. Jin-Yun Yang
8. Aly R. Seadawy

Citations in the corpus

• New extended auxiliary equation method for finding many new Jacobi elliptic function solutions of three nonlinear Schrödinger equations (2017, methodology): “A variety of powerful methods, such as the inverse scattering method,[1] the Hirota bilinear transform method,[2] the truncated Painlevé expansion method,[3,4] Bäcklund transformation,[5,6] the exp-function method,[7–11] the Jacobi elliptic function expansion method,[12–15] the ( G′/G ) -expansionme”
• Solving the (3 + 1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm (2012, methodology): “Then applying the multiple exp-function algorithm [4], we obtain by Maple: a1 1⁄4 ða2 1Þk1 ð3:6Þ and so, the resulting one-wave solutions read”
• The exp(-Φ(ξ))-expansion method for finding travelling wave solutions of Vakhnenko-Parkes equation (2014, methodology): “, 2010), the multiple exp-function method (Ma et al., 2010; Ma and Zhu 2012), Bernoulli Sub-ODE Method (Marzan et al.”