Integrable nonlocal Hirota equations
نویسندگان
چکیده
منابع مشابه
Solutions of Non-Integrable Equations by the Hirota Direct Method
We show that we can also apply the Hirota method to some nonintegrable equations. For this purpose, we consider the extensions of the Kadomtsev-Petviashvili (KP) and the Boussinesq (Bo) equations. We present several solutions of these equations.
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Various connections between 2-D gravity and KdV, dKdV, inverse scattering, etc. are established. For KP we show how to extract from the dispersionless limit of the Fay differential identity of Takasaki-Takebe the collection of differential equations for F = log(τ ) which play the role of Hirota type equations in the dispersionless theory. 1. HIROTA EQUATIONS In [7] we showed how second derivati...
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A new integrable nonlocal nonlinear Schrödinger equation is introduced. It possesses a Lax pair and an infinite number of conservation laws and is PT symmetric. The inverse scattering transform and scattering data with suitable symmetries are discussed. A method to find pure soliton solutions is given. An explicit breathing one soliton solution is found. Key properties are discussed and contras...
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The dispersionless differential Fay identity is shown to be equivalent to a kernel expansion providing a universal algebraic characterization and solution of the dispersionless Hirota equations. Some calculations based on D-bar data of the action are also indicated.
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A brief non-technical review of the recent study [1] of classical integrable structures in quantum integrable systems is given. It is explained how to identify the standard objects of quantum integrable systems (transfer matrices, Baxter's Q-operators, etc) with elements of classical non-linear integrable difference equations (τ-functions, Baker-Akhiezer functions, etc). The nested Bethe ansatz...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2019
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.5013154