Symbolic algorithms for the Painlevé test, special solutions, and recursion operators for nonlinear PDEs. This paper discusses the algorithms and implementations of three MATHEMATICA packages for the study of integrability and the computation of closed-form solutions of nonlinear polynomial partial differential equations (PDEs). The first package, PainleveTest.m, symbolically performs the Painlevé integrability test. The second package, PDESpecialSolutions.m, computes exact solutions expressible in hyperbolic or elliptic functions. The third package, PDERecursionOperator.m, generates and tests recursion operators.

References in zbMATH (referenced in 23 articles , 2 standard articles )

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  1. Wazwaz, Abdul-Majid: Multiple complex soliton solutions for integrable negative-order KdV and integrable negative-order modified KdV equations (2019)
  2. Wazwaz, Abdul-Majid: Negative-order integrable modified KdV equations of higher orders (2018)
  3. Wazwaz, Abdul-Majid: Painlevé analysis for a new integrable equation combining the modified Calogero-Bogoyavlenskii-Schiff (MCBS) equation with its negative-order form (2018)
  4. Wazwaz, Abdul-Majid: Negative-order KdV and negative-order KP equations: multiple soliton solutions (2017)
  5. Zhu, Shundong; Shen, Shoufeng; Jin, Yongyang; Li, Chunxia; Ma, Wen-Xiu: New soliton hierarchies associated with the real Lie algebra (\mathrmso(4,\mathbbR)) (2017)
  6. Wazwaz, Abdul-Majid; Xu, Gui-Qiong: Negative-order modified KdV equations: multiple soliton and multiple singular soliton solutions (2016)
  7. Jiang, Liya; Jin, Yongyang; Ma, Wen-Xiu; Shen, Shoufeng; Zhu, Haiyan: Novel soliton hierarchies of Levi type and their bi-Hamiltonian structures (2015)
  8. Shen, Shoufeng; Jiang, Liya; Jin, Yongyang; Ma, Wen-Xiu: New soliton hierarchies associated with the Lie algebra so(3,(\mathbbR)) and their Bi-Hamiltonian structures (2015)
  9. Wang, Yun-Po; Tian, Bo; Wang, Ming; Wang, Yu-Feng; Sun, Ya; Xie, Xi-Yang: Bäcklund transformations and soliton solutions for a ((2+1))-dimensional Korteweg-de Vries-type equation in water waves (2015)
  10. Wazwaz, Abdul-Majid: A variety of ((3+1))-dimensional Burgers equations derived by using the Burgers recursion operator (2015)
  11. Zhu, Haiyan; Yu, Shuimeng; Shen, Shoufeng; Ma, Wen-Xiu: New integrable (\mathrmsl(2,\mathbbR))-generalization of the classical Wadati-Konno-Ichikawa hierarchy (2015)
  12. Shirvani-Sh, Vahid; Nadjafikhah, Mehdi: Conservation laws and exact solutions of the Whitham-type equations (2014)
  13. Wazwaz, Abdul-Majid: A variety of ((3+1))-dimensional mKdV equations derived by using the mKdV recursion operator (2014)
  14. Ma, Wen-Xiu: A soliton hierarchy associated with (\mathrmso(3,\mathbbR)) (2013)
  15. Naz, Rehana; Naeem, Imran; Khan, M. Danish: Conservation laws of some physical models via symbolic package GeM (2013)
  16. Wazwaz, Abdul-Majid: ((2+1))-dimensional Burgers equations (\mathrmBE(m+n+1)): using the recursion operator (2013)
  17. Wazwaz, Abdul-Majid: A study on the ((2+1))-dimensional KdV4 equation derived by using the KdV recursion operator (2013)
  18. Wazwaz, Abdul-Majid: ((2+1))-dimensional mKdV (N) equations by the mKdV recursion operator: multiple soliton and multiple singular soliton solutions (2012)
  19. Poole, Douglas; Hereman, Willy: Symbolic computation of conservation laws for nonlinear partial differential equations in multiple space dimensions (2011)
  20. Bagchi, Bijan; Das, Supratim; Ganguly, Asish: New exact solutions of a generalized shallow water wave equation (2010)

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