Symbolic computation of the Painlevé test for nonlinear partial differential equations using Maple. A software package wkptest written in Maple is presented, which can carry out the traditional Painlevé test for polynomial partial differential equations automatically. Furthermore, some truncated expansions are also obtained whether an equation passes the test or not. The truncated expansions play an important role in studying the integrability, such as Lax pairs, bilinear forms, Darboux transformations and explicit solutions. The effectiveness of wkptest is illustrated by applying it to a variety of equations.

References in zbMATH (referenced in 16 articles , 1 standard article )

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  1. Saleh, R.; Mabrouk, S. M.; Kassem, M.: Truncation method with point transformation for exact solution of Liouville Bratu Gelfand equation (2018)
  2. Ohno, Yuji; Yoshida, Zensho: Nonlinear ion acoustic waves scattered by vortexes (2016)
  3. Wazwaz, Abdul-Majid; El-Tantawy, S. A.: A new integrable ((3+1))-dimensional KdV-like model with its multiple-soliton solutions (2016)
  4. Wazwaz, Abdul-Majid; Xu, Gui-qiong: An extended modified KdV equation and its Painlevé integrability (2016)
  5. Xu, Gui-Qiong; Wazwaz, Abdul-Majid: New bilinearization, Bäcklund transformation and infinite conservation laws for the KdV6 equation with Bell polynomials (2016)
  6. Xu, Pengbo; Gao, Yitian; Gai, Xiaoling; Meng, Dexin; Shen, Yujia; Wang, Lei: Soliton solutions, Bäcklund transformation and Wronskian solutions for the extended ((2+1))-dimensional Konopelchenko-Dubrovsky equations in fluid mechanics (2011)
  7. Zhou, Zhen-jiang; Fu, Jing-zhi; Li, Zhi-bin: Maple packages for computing Hirota’s bilinear equation and multisoliton solutions of nonlinear evolution equations (2010)
  8. Xu, Gui-Qiong: A note on the Painlevé test for nonlinear variable-coefficient PDEs (2009)
  9. Zhao, Yin-Long; Liu, Yin-Ping; Li, Zhi-Bin: A modified WTC algorithm for the Painlevé test of nonlinear variable-coefficient PDEs (2009)
  10. An, Hong-Li; Chen, Yong: Numerical complexiton solutions for the complex KdV equation by the homotopy perturbation method (2008)
  11. Wan, Ying; Song, Lina; Yin, Li; Zhang, Hongqing: Generalized method and new exact wave solutions for ((2 + 1))-dimensional Broer-Kaup-Kupershmidt system (2007)
  12. Vernov, S. Yu.: Construction of exact partial solutions of nonintegrable systems by means of formal Laurent and Puiseux series (2006)
  13. Yao, Ruo-Xia; Li, Zhi-Bin: CONSLAW: A Maple package to construct the conservation laws for nonlinear evolution equations (2006)
  14. Zhou, Zhen-Jiang; Fu, Jing-Zhi; Li, Zhi-Bin: An implementation for the algorithm of Hirota bilinear form of PDE in the Maple system (2006)
  15. Xu, Gui-qiong; Li, Zhi-bin: PDEPtest: a package for the Painlevé test of nonlinear partial differential equations (2005)
  16. Xu, Gui-Qiong; Li, Zhi-Bin: Symbolic computation of the Painlevé test for nonlinear partial differential equations using Maple (2004)