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Rogers, C. and Schief, W.K. (2002) Bäcklund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory. Cambridge University Press.

has been cited by the following article:

• TITLE: High-Order Solitons and Hybrid Behavior of (3 + 1)-Dimensional Potential Yu-Toda-Sasa-Fukuyama Equation with Variable Coefficients

  AUTHORS: Xiyu Tan, Xingying Li

  KEYWORDS: Variable-Coefficient YTSF Equation, Hirota Bilinear Method, N-Soliton, Hybrid Solution

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.8, August 8, 2024

  ABSTRACT: In this paper, some exact solutions of the (3 + 1)-dimensional variable-coefficient Yu-Toda-Sasa-Fukuyama equation are investigated. By using Hirota’s direct method and symbolic computation, we obtained N-soliton solution. By using the long wave limit method, the N-order rational solution can be obtained from N-order soliton solution. Then, through the paired complexification of parameters, the lump solution is obtained from N-order rational solution. Meanwhile, we obtained a hybrid solution between 1-lump solution and N-soliton ( N=1,2 ) by using the long wave limit method and parameter complex. Furthermore, four different sets of three-dimensional graphs of solitons, lump solutions and hybrid solutions are drawn by selecting four different sets of coefficient functions which include one set of constant coefficient function and three sets of variable coefficient functions.