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; Bilinearization; HIROTA.MAX; HBFTrans2; Matlab; WKPtest; CONSLAW; Dirac_Laczos; HBFGen; GeM; Epsilon; CharSets; Rif; PDEtools; GiNaC Cited in: 208 Publications 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 0948.76595Parkes, E. J.; Duffy, B. R. 1996 all top 5 Cited by 266 Authors 24 Kudryashov, Nikolaĭ Alekseevich 11 Zhang, Huiqun 8 Fan, Engui 7 Hon, Yiu-Chung 7 Kaya, Doǧan 7 Parkes, E. John 7 Wazwaz, Abdul-Majid Abdul-Rahman 7 Zhang, Hongqing 5 Wei, Long 4 Li, Bangqing 4 Ma, Yulan 4 Sinelshchikov, Dmitry I. 4 Younis, Muhammad 4 Zayed, Elsayed M. E. 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 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, Ibrahim E. 2 Kavitha, Louis 2 Khalfallah, Mohammed 2 Khalique, Chaudry Masood 2 Khater, Ahmed H. 2 Kochanov, Mark B. 2 Kumar, Rajeev 2 Li, Biao 2 Li, Lingxiao 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 Vinodh, D. 2 Wang, Dan 2 Wang, Liang-Bi 2 Wu, Xiang 2 Yang, Zonghang 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 Ali, Ahmad Tawfik 1 Ali, Ahmed Hassan Ahmed 1 Alurrfi, Khaled A. E. 1 Alvarez, F. Xavier 1 Aly, Emad H. 1 Amin, Muhammad 1 Antonova, Anastasia O. 1 Arbabi, Somayeh 1 Bafaluy, Javier 1 Bai, Chenglin 1 Bai, Yongbin 1 Baldwin, Douglas E. 1 Baskonus, Haci Mehmet 1 Bekir, Ahmet 1 Bermudez, German Rodriguez 1 Bikulciene, Liepa 1 Bilige, Sudao 1 Biswas, Anjan 1 Callebaut, Dirk K. 1 Ceballos, Juan Carlos 1 Chang, Haixia 1 Chaolu, Temuer 1 Dai, Chaoqing 1 Dai, Zhengde 1 Das, Amiya 1 Delkhosh, Mehdi 1 Deng, Aiping 1 Dhamayanthi, S. 1 Ding, Xuanhao ...and 166 more Authors all top 5 Cited in 42 Serials 78 Applied Mathematics and Computation 24 Chaos, Solitons and Fractals 23 Communications in Nonlinear Science and Numerical Simulation 6 Computers & Mathematics with Applications 6 Journal of Computational and Applied Mathematics 6 Nonlinear Dynamics 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 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 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 Waves in Random and Complex Media 1 Nonlinear Analysis. Hybrid Systems 1 Journal of Nonlinear Science and Applications all top 5 Cited in 19 Fields 192 Partial differential equations (35-XX) 35 Numerical analysis (65-XX) 26 Dynamical systems and ergodic theory (37-XX) 15 Ordinary differential equations (34-XX) 14 Fluid mechanics (76-XX) 7 Computer science (68-XX) 6 Optics, electromagnetic theory (78-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 Field theory and polynomials (12-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 Relativity and gravitational theory (83-XX) Citations by Year