ATFM

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.


References in zbMATH (referenced in 209 articles , 1 standard article )

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  1. Mithun Bairagi: GiNaCDE: the high-performance F-expansion and First Integral Methods with C++ library for solving Nonlinear Differential Equations (2022) not zbMATH
  2. Xu, Guoan; Zhang, Yi; Li, Jibin: Exact solitary wave and periodic-peakon solutions of the complex Ginzburg-Landau equation: dynamical system approach (2022)
  3. Baskonus, Haci Mehmet; García Guirao, Juan Luis; Kumar, Ajay; Vidal Causanilles, Fernando S.; Bermudez, German Rodriguez: Regarding new traveling wave solutions for the mathematical model arising in telecommunications (2021)
  4. Das, Amiya; Mandal, Uttam Kumar: Integrability, bilinearization, solitons and exact three wave solutions for a forced Korteweg-de Vries equation (2021)
  5. Kumar, Rajeev; Ram, Gurdas; Bansal, Anupma: Painlevé analysis and invariant solutions of variable coefficients extended Ostrovsky equation (2021)
  6. Leta, Temesgen Desta; Liu, Wenjun; Achab, Abdelfattah El; Rezazadeh, Hadi; Bekir, Ahmet: Dynamical behavior of traveling wave solutions for a ((2+1))-dimensional Bogoyavlenskii coupled system (2021)
  7. Neirameh, Ahmad: Solitary wave solutions to the multidimensional Landau-Lifshitz equation (2021)
  8. Neirameh, Ahmad; Eslami, Mostafa; Mehdipoor, Mostafa: New types of soliton solutions for space-time fractional cubic nonlinear Schrodinger equation (2021)
  9. Sciacca, M.; Alvarez, F. X.; Jou, D.; Bafaluy, J.: Thermal solitons along wires with flux-limited lateral exchange (2021)
  10. Sciacca, Michele: Two relaxation times and thermal nonlinear waves along wires with lateral heat exchange (2021)
  11. Yépez-Martínez, H.; Khater, Mostafa M. A.; Rezazadeh, Hadi; Inc, Mustafa: Analytical novel solutions to the fractional optical dynamics in a medium with polynomial law nonlinearity and higher order dispersion with a new local fractional derivative (2021)
  12. Kudryashov, Nikolay A.: Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations (2020)
  13. Kudryashov, Nikolay A.: First integrals and general solution of the complex Ginzburg-Landau equation (2020)
  14. Shi, Dandan; Zhang, Yufeng; Liu, Wenhao: Multiple exact solutions of the generalized time fractional foam drainage equation (2020)
  15. Vinodh, D.; Asokan, R.: Multi-soliton, rogue wave and periodic wave solutions of generalized ((2+1)) dimensional Boussinesq equation (2020)
  16. Delkhosh, Mehdi; Parand, Kourosh: A hybrid numerical method to solve nonlinear parabolic partial differential equations of time-arbitrary order (2019)
  17. Ha, Jinting; Zhang, Huiqun; Zhao, Qiulan: Exact solutions for a Dirac-type equation with N-fold Darboux transformation (2019)
  18. Kudryashov, Nikolay A.: Exact solutions of the equation for surface waves in a convecting fluid (2019)
  19. Kudryashov, Nikolay A.; Safonova, Dariya V.; Biswas, Anjan: Painlevé analysis and a solution to the traveling wave reduction of the Radhakrishnan-Kundu-Lakshmanan equation (2019)
  20. Mancas, Stefan C.: Traveling wave solutions to Kawahara and related equations (2019)

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