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ATFM

swMATH ID: 42146
Software Authors: Parkes, E. J.; Duffy, B. R.
Description: An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations. The tanh-function method for finding explicit travelling solitary wave solutions to non-linear evolution equations is described. The method is usually extremely tedious to use by hand. We present a Mathematica package ATFM that deals with the tedious algebra and outputs directly the required solutions. The use of the package is illustrated by applying it to a variety of equations; not only are previously known solutions recovered but in some cases more general forms of solution are obtained.
Homepage: https://www.sciencedirect.com/science/article/abs/pii/001046559600104X
Dependencies: Mathematica
Related Software: MACSYMA; Maple; RATH; PDESpecialSolutions; Mathematica; RAEEM; WKPtest; Bilinearization; HIROTA.MAX; HBFTrans2; Matlab; GiNaC; GiNaCDE; CONSLAW; GeM; Epsilon; Dirac_Laczos; HBFGen; CharSets; Rif
Cited in: 218 Documents

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
An automated \(\tanh\)-function method for finding solitary wave solutions to nonlinear evolution equations. Zbl 0948.76595
Parkes, E. J.; Duffy, B. R.
1996
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Cited by 283 Authors

25 Kudryashov, Nikolaĭ Alekseevich
11 Zhang, Huiqun
8 Fan, Engui
8 Wazwaz, Abdul-Majid Abdul-Rahman
7 Hon, Yiu-Chung
7 Kaya, Doǧan
7 Parkes, E. John
7 Zhang, Hongqing
5 Wei, Long
5 Zayed, Elsayed M. E.
4 Li, Bangqing
4 Ma, Yulan
4 Sinelshchikov, Dmitry I.
4 Younis, Muhammad
3 Ali, Safdar
3 Ebaid, Abdelhalim
3 Feng, Zhaosheng
3 Guo, Shimin
3 He, Yinghui
3 Ma, Hongcai
3 Neirameh, Ahmad
3 Raslan, Kamal Raslan
3 Wang, Mingliang
3 Wang, Yang
3 Wen, Xiaoyong
3 Zakharchenko, Anastasia S.
3 Zhou, Yubin
2 Abdusalam, H. A.
2 Ali Akbar, M.
2 Amer, Yasser A.
2 Asokan, Raghavan
2 Bansal, Anupma
2 Biswas, Anjan
2 Chen, Yong
2 Darvishi, Mohammad Taghi
2 Demina, Maria V.
2 El-Sayed, Salah M.
2 Fahmy, E. S.
2 Guo, Peng
2 Hayek, Mohamed
2 Huang, Dingjiang
2 Inan, İbrahim Enam
2 Kavitha, Louis
2 Khalique, Chaudry Masood
2 Khater, Ahmed H.
2 Kochanov, Mark B.
2 Kumar, Rajeev
2 Li, Biao
2 Li, Lingxiao
2 Li, Zhibin
2 Liu, Zhengrong
2 Loguinova, Nadejda B.
2 Long, Yao
2 Ma, Wen-Xiu
2 Rezazadeh, Hadi
2 Ryabov, Pavel N.
2 Sayed, S. M.
2 Sciacca, Michele
2 Soliman, Ahmed Abo-Elmagd
2 Ünsal, Ömer
2 Vinodh, D.
2 Wang, Dan
2 Wang, Liang-Bi
2 Wu, Xiang
2 Yang, Zonghang
2 Yépez-Martínez, Huitzilin
2 Yu, Xiuqing
2 Zhang, Bengong
2 Zhang, Lijun
1 Abassy, Tamer A.
1 Abbas, Muhammad Mohsin
1 Abdel-Rady, A. S.
1 Abdelhamid, Hamdi M.
1 Abdelwahed, H. G.
1 Abulwafa, Essam M.
1 Aderogba, Adebayo Abiodun
1 Ali, Ahmad Tawfik
1 Ali, Ahmed Hassan Ahmed
1 Alurrfi, Khaled A. E.
1 Alvarez, F. Xavier
1 Aly, Emad H.
1 Alzahrani, Abdullah Khamis Hassan
1 Amin, Muhammad Shoib
1 Antonova, Anastasia O.
1 Arbabi, Somayeh
1 Arora, Rajan
1 Arshed, Saima
1 Bafaluy, Javier
1 Bai, Chenglin
1 Bai, Yongbin
1 Baldwin, Douglas E.
1 Baskonus, Haci Mehmet
1 Bekir, Ahmet
1 Belić, Milivoj R.
1 Bermudez, German Rodriguez
1 Bikulciene, Liepa
1 Bilige, Sudao
1 Callebaut, Dirk K.
1 Ceballos, Juan Carlos
1 Chang, Haixia
...and 183 more Authors
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Cited in 48 Serials

78 Applied Mathematics and Computation
24 Chaos, Solitons and Fractals
23 Communications in Nonlinear Science and Numerical Simulation
7 Nonlinear Dynamics
6 Computers & Mathematics with Applications
6 Journal of Computational and Applied Mathematics
5 Abstract and Applied Analysis
4 Journal of Applied Mathematics
4 Advances in Difference Equations
3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
3 Acta Applicandae Mathematicae
3 Applied Mathematics. Series B (English Edition)
3 Mathematical Problems in Engineering
3 Advances in Mathematical Physics
3 International Journal of Applied and Computational Mathematics
2 Applied Mathematics Letters
2 Computational Mathematics and Modeling
2 Regular and Chaotic Dynamics
2 Boletim da Sociedade Paranaense de Matemática. Terceira Série
2 Waves in Random and Complex Media
2 Chinese Journal of Physics (Taipei)
2 Communications in Theoretical Physics
2 Journal of Applied Analysis and Computation
2 Cogent Mathematics
1 Computers and Fluids
1 Computer Physics Communications
1 Journal of Mathematical Physics
1 Physica A
1 Physics Letters. A
1 Reports on Mathematical Physics
1 Wave Motion
1 Mathematics and Computers in Simulation
1 Quaestiones Mathematicae
1 Journal of the Nigerian Mathematical Society
1 Physica D
1 Acta Mathematicae Applicatae Sinica. English Series
1 Journal of Symbolic Computation
1 Science in China. Series A
1 Applied Mathematical Modelling
1 Computational and Applied Mathematics
1 Fractals
1 Differential Equations and Dynamical Systems
1 Qualitative Theory of Dynamical Systems
1 Nonlinear Analysis. Hybrid Systems
1 Journal of Nonlinear Science and Applications
1 Communications in Mathematics
1 Caspian Journal of Mathematical Sciences
1 Applied Mathematics and Nonlinear Sciences
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Cited in 19 Fields

203 Partial differential equations (35-XX)
37 Numerical analysis (65-XX)
29 Dynamical systems and ergodic theory (37-XX)
14 Ordinary differential equations (34-XX)
13 Fluid mechanics (76-XX)
9 Optics, electromagnetic theory (78-XX)
8 Computer science (68-XX)
4 Special functions (33-XX)
4 Statistical mechanics, structure of matter (82-XX)
3 Mechanics of deformable solids (74-XX)
3 Quantum theory (81-XX)
2 Classical thermodynamics, heat transfer (80-XX)
2 Biology and other natural sciences (92-XX)
1 Nonassociative rings and algebras (17-XX)
1 Real functions (26-XX)
1 Differential geometry (53-XX)
1 Global analysis, analysis on manifolds (58-XX)
1 Probability theory and stochastic processes (60-XX)
1 Relativity and gravitational theory (83-XX)

Citations by Year