Hints on the Hirota Bilinear Method
نویسندگان
چکیده
منابع مشابه
Hirota Bilinear Formalism and Supersymmetry
Extending the gauge-invariance principle for τ functions of the standard bilinear formalism to the supersymmetric case, we define N = 1 supersymmetric Hirota operators. Using them, we bilinearize SUSY nonlinear evolution equations. The super-soliton solutions and extension to SUSY sine-Gordon are also discussed. As a quite strange paradox it is shown that the Lax integrable SUSY KdV of Manin-Ra...
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The finite-genus solutions for the Hirota's bilinear difference equation are constructed using the Fay's identities for the θ-functions of compact Riemann surfaces. In the present work I want to consider once more the question of constructing the finite-genus solutions for the famous Hirota's bilinear difference equation (HBDE) [1] which has been solved in [2] using the so-called algebraic-geom...
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Physically relevant soliton solutions of the resonant nonlinear Schrodinger (RNLS) equation with nontrivial boundary conditions, recently proposed for description of uniaxial waves in a cold collisionless plasma, are considered in the Hirota bilinear approach. By the Madelung representation, the model transformed to the reaction-diffusion analog of the NLS equation for which the bilinear repres...
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The investigation of the exact solutions of nonlinear equations plays an important role in the study of nonlinear physical phenomena. For example, the wave phenomena observed in fluid dynamics, plasma and elastic media are often modelled by the bell shaped sech solutions and the kink shaped tanh traveling wave solutions. The exact solution, if available, of those nonlinear equations facilitates...
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A linear superposition principle of exponential traveling waves is analyzed for Hirota bilinear equations, with an aim to construct a specific sub-class of N-soliton solutions formed by linear combinations of exponential traveling waves. Applications are made for the 3 + 1 dimensional KP, Jimbo–Miwa and BKP equations, thereby presenting their particular N-wave solutions. An opposite question is...
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ژورنال
عنوان ژورنال: Acta Physica Polonica A
سال: 2007
ISSN: 0587-4246,1898-794X
DOI: 10.12693/aphyspola.112.1171