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Neugebauer-Kramer solutions of the Ernst equation in Hirota's direct method

Journal of Physics A: Mathematical and General, 1998
Summary: We prove analytically the Sasa-Satsuma conjecture which states that their solution of bilinear form of the Ernst equation gives the Neugebauere-Kramer solution in particular cases. This proof relates Hirota's direct method with the Bäcklund transformation method and opens the way towards the comprehensive interpretation of the Ernst equation.
Masuda, Tetsu, Sasa, Narimasa, Fukuyama, Takeshi +2 more
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Soliton Solutions of Coupled KdV System from Hirota's Bilinear Direct Method

Communications in Theoretical Physics, 2008
With Hirota's bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges
Yang Jian-Rong, Mao Jie-Jian
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Optical solitons and complexitons for generalized Schrödinger–Hirota model by the modified extended direct algebraic method