PDEBellII

PDEBellII: a Maple package for finding bilinear forms, bilinear Bäcklund transformations, Lax pairs and conservation laws of the KdV-type equations. Based on the Bell polynomials scheme, this paper presents a Maple computer algebra program PDEBellII which can automatically construct the bilinear forms, bilinear Bäcklund transformations, Lax pairs and conservation laws of the KdV-type soliton equations. Some examples are given to verify the validity of our program.


References in zbMATH (referenced in 11 articles , 1 standard article )

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  1. Yaşar, Emrullah; Yıldırım, Yakup; Adem, Abdullahi Rashid: Extended transformed rational function method to nonlinear evolution equations (2019)
  2. Wang, Xiu-Bin; Tian, Shou-Fu; Feng, Lian-Li; Zhang, Tian-Tian: On quasi-periodic waves and rogue waves to the ((4+1))-dimensional nonlinear Fokas equation (2018)
  3. Wang, Xiu-Bin; Tian, Shou-Fu; Feng, Lian-Li; Yan, Hui; Zhang, Tian-Tian: Quasiperiodic waves, solitary waves and asymptotic properties for a generalized ((3+1))-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation (2017)
  4. Yıldırım, Yakup; Yaşar, Emrullah: An extended Korteweg-de Vries equation: multi-soliton solutions and conservation laws (2017)
  5. Singh, Manjit; Gupta, R. K.: Exact solutions for nonlinear evolution equations using novel test function (2016)
  6. Tu, Jian-Min; Tian, Shou-Fu; Xu, Mei-Juan; Ma, Pan-Li; Zhang, Tian-Tian: On periodic wave solutions with asymptotic behaviors to a ((3+1))-dimensional generalized B-type Kadomtsev-Petviashvili equation in fluid dynamics (2016)
  7. Wang, Xiu-Bin; Tian, Shou-Fu; Xua, Mei-Juan; Zhang, Tian-Tian: On integrability and quasi-periodic wave solutions to a ((3+1))-dimensional generalized KdV-like model equation (2016)
  8. Xu, Mei-Juan; Tian, Shou-Fu; Tu, Jian-Min; Zhang, Tian-Tian: Bäcklund transformation, infinite conservation laws and periodic wave solutions to a generalized ((2+1))-dimensional Boussinesq equation (2016)
  9. Li, He; Gao, Yi-Tian; Liu, Li-Cai: Bell-polynomial approach and soliton solutions for some higher-order Korteweg-de Vries equations in fluid mechanics, plasma physics and lattice dynamics (2015)
  10. Miao, Qian; Wang, Yunhu; Chen, Yong; Yang, Yunqing: \textitPDEBellII: a Maple package for finding bilinear forms, bilinear Bäcklund transformations, Lax pairs and conservation laws of the KdV-type equations (2014)
  11. Wang, Yun-Hu; Wang, Hui; Temuer, Chaolu: Lax pair, conservation laws, and multi-shock wave solutions of the DJKM equation with Bell polynomials and symbolic computation (2014)