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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.
https://doi.org/10.1017/cbo9780511606359

has been cited by the following article:

• TITLE: New Lump Solution and Their Interactions with N-Solitons for a Shallow Water Wave Equation

  AUTHORS: Yin Ji, Xiyu Tan

  KEYWORDS: HSI Equation, Breather-Waves, Lump Solutions, Interaction Solution

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.8, August 16, 2024

  ABSTRACT: By employing the Hirota’s bilinear method and different test functions, the breather solutions of HSI equation with different structures are obtained based on symbolic calculation with perturbation parameters. Some new lump solitons are found in the process of studying the degradation behavior of breather solutions. The interaction between lump solution and soliton solution is constructed in the form of lump solution, and the motion trajectory of lump is obtained. In addition, the theorem of lump solitons and N-solitons superposition is given and proved. The superposition formula of lump is derived from the theorem, and its spatial evolution behavior is given.