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Hirota bilinear method for nonlinear evolution equations
2003Summary. The bilinear method introduced by Hirota to obtain exact solutions for nonlinear evolution equations is discussed. Firstly, several examples including the Korteweg-deVries, nonlinear Schrodinger and Toda equations are given to show how solutions are derived.
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Hirota’s Bilinear Method and Its Connection with Integrability
2008We 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
1978Although 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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Long-time asymptotic for the Hirota equation via nonlinear steepest descent method
Nonlinear Analysis: Real World Applications, 2015, Engui Fan
exaly
NDouble Pole Solution for the Modified Korteweg-de Vries Equation by the Hirota's Method
Journal of the Physical Society of Japan, 1989Kimiaki Konno, Konno Kimiaki
exaly