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Hirota’s Bilinear Method and Its Connection with Integrability

2008
We give an introduction to Hirota’s bilinear method, which is particularly efficient for constructing multisoliton solutions to integrable nonlinear evolution equations. We discuss in detail how the method works for equations in the Korteweg–de Vries class and then go through some other classes of equations.
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Hirota’s Method of Solving Soliton-Type Equations

1978
Although it is a gross oversimplification to say that Hirota’s method amounts to guesswork, this is basically true. It is extremely useful when more sophisticated methods have failed. Its principal drawback (apart from the guesswork element) is that it gives only soliton solutions and no background (or ‘radiation’).
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N-double poles solutions for nonlocal Hirota equation with nonzero boundary conditions using Riemann–Hilbert method and PINN algorithm

Physica D: Nonlinear Phenomena, 2022
Yong Chen
exaly

Nondegenerate solitons and collision dynamics of the variable-coefficient coupled higher-order nonlinear Schrödinger model via the Hirota method

Applied Mathematics Letters, 2022
Da-Sheng Mou, Chao-Qing Dai
exaly

An extended Hirota bilinear method and new wave structures of (2+1)-dimensional Sawada–Kotera equation

Applied Mathematics Letters, 2023
Ruoxia Yao, S Y Lou
exaly

Multiple-soliton solutions for the KP equation by Hirota’s bilinear method and by the tanh–coth method

Applied Mathematics and Computation, 2007
Abdul-Majid Wazwaz
exaly

Long-time asymptotic for the Hirota equation via nonlinear steepest descent method

Nonlinear Analysis: Real World Applications, 2015
Engui Fan
exaly

The Periodic Hirota Method

2010
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