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Hirota’s Bilinear Method and Partial Integrability
1990We discuss Hirota’s bilinear method from the point of view of partial integrability. Many different levels of integrability are shown to exist.
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The Hirota Method and Soliton Solutions to the Multidimensional Nonlinear Schrodinger Equation
Siberian Mathematical Journal, 2002By using the Hirota method the author finds one-soliton solutions to the generalized \(3+1\) nonlinear Schrödinger equation \[ i \psi_t = \psi_{xy} + \psi_{xz} + V \psi, \qquad V_x = 2((|\psi|^2)_y + (|\psi|^2)_z) \] derived by R. Myrzakulov. Notice that in the variables \(x, \eta = (y+z)/2, \xi = (y-z)/2\) this system takes the following \(2+1\) form:
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New ways of applying the Hirota method in soliton theory
1996info:eu-repo/semantics ...
Loris, Ignace +2 more
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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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NDouble Pole Solution for the Modified Korteweg-de Vries Equation by the Hirota's Method
Journal of the Physical Society of Japan, 1989Kimiaki Konno
exaly
The simplified Hirota’s method for studying three extended higher-order KdV-type equations
Journal of Ocean Engineering and Science, 2016Abdul-Majid Wazwaz
exaly