Results 161 to 170 of about 2,478 (193)

Method for Generating Discrete Soliton Equation. III

Journal of the Physical Society of Japan, 1982
A method is given for generating hierarchies of soliton equations on which infinite dimensional subalgebras of \({\mathfrak gl}(\infty)\) act infinitesimally. Various choices of subalgebras and discrete or continuous time evolutions lead to a variety of difference or differential equations.
Date, E., Jimbo, M., Miwa, T.
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Bilinearization of Soliton Equations

Journal of the Physical Society of Japan, 1982
Transformations of soliton equations into the bilinear forms involving four dependent variables are discussed. It is found that both nonlinear Schrodinger equation and classical Heisenberg ferromagnet equation are transformed into the same bilinear from, while the equation \begin{aligned} \phi_{xt}{=}\phi(1-|\phi_{t}|^{2})^{1/2} \end{aligned} shares ...
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Soliton solutions of Burgers equations and perturbed Burgers equation

Applied Mathematics and Computation, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anwar Ja'afar Mohamad Jawad, Marko D. Petkovic, Anjan Biswas   +2 more
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Geometrization of soliton equations

Physics Letters A, 1979
Abstract A unified geometric picture of the soliton equations is presented. All the soliton equations in 1 + 1 dimensions that can be solved by the inverse scattering methods (e.g. sine-Gordon, Korteweg-de Vries and modified Korteweg-de Vries equations) are shown to describe pseudospherical surfaces, i.e.
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Soliton and Algebraic Equation

Journal of the Physical Society of Japan, 1982
The close relationship between the soliton and the algebraic equation is found in the case of the Benjamin-Ono equation. Many interesting formulas are presented concerning the algebra of the zeros of the Laguerre polynomial.
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Soliton states of Maxwell’s equations and nonlinear Schrödinger equation

Science in China Series A: Mathematics, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Soliton solutions of the shifted nonlocal NLS and MKdV equations

Physics Letters, Section A: General, Atomic and Solid State Physics, 2022
Metin Gurses, Asli Pekcan
exaly  

The Classical Soliton Equations

2003
Abstract An exciting development in nonlinear science during the 1970s was the gradual realization that certain nonlinear partial differential equations display a variety of exact solutions. These include not only solitary waves-known since the nineteenth century studies of Russell, Bazin, and Boussinesq—but solutions involving an ...
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Two new types of nonlocal Boussinesq equations in water waves: Bright and dark soliton solutions

Chinese Journal of Physics, 2022
Bang-Qing Li, Abdul-Majid Wazwaz, Yu-Lan Ma   +2 more
exaly  

Nonlocal modified KdV equations and their soliton solutions by Hirota Method

Communications in Nonlinear Science and Numerical Simulation, 2019
Metin Gurses, Asli Pekcan
exaly