Analytical integrability and physical solutions of d-KdV equation

Karmakar, P K; Dwivedi, C B

doi:10.1063/1.2173087

Title: Analytical integrability and physical solutions of d-KdV equation

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Abstract

A new idea of electron inertia-induced ion sound wave excitation for transonic plasma equilibrium has already been reported. In such unstable plasma equilibrium, a linear source driven Korteweg-de Vries (d-KdV) equation describes the nonlinear ion sound wave propagation behavior. By numerical techniques, two distinct classes of solution (soliton and oscillatory shocklike structures) are obtained. Present contribution deals with the systematic methodological efforts to find out its (d-KdV) analytical solutions. As a first step, we apply the Painleve method to test whether the derived d-KdV equation is analytically integrable or not. We find that the derived d-KdV equation is indeed analytically integrable since it satisfies Painleve property. Hirota's bilinearization method and the modified sine-Gordon method (also termed as sine-cosine method) are used to derive the analytical results. Perturbative technique is also applied to find out quasistationary solutions. A few graphical plots are provided to offer a glimpse of the structural profiles obtained by different methods applied. It is conjectured that these solutions may open a new scope of acoustic spectroscopy in plasma hydrodynamics.

Authors:

Karmakar, P K; Dwivedi, C B ^[1]

Centre of Plasma Physics, Tepesia, Sonapur, Guwahati-482 402, Assam, Bharat (India)

Publication Date:: Wed Mar 15 00:00:00 EST 2006

OSTI Identifier:: 20768741

Resource Type:: Journal Article

Journal Name:: Journal of Mathematical Physics

Additional Journal Information:: Journal Volume: 47; Journal Issue: 3; Other Information: DOI: 10.1063/1.2173087; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; ELECTRONS; EQUILIBRIUM; EXCITATION; HYDRODYNAMICS; INTEGRAL CALCULUS; ION ACOUSTIC WAVES; KORTEWEG-DE VRIES EQUATION; MOMENT OF INERTIA; NONLINEAR PROBLEMS; PLASMA; SINE-GORDON EQUATION; SOLITONS; SOUND WAVES; SPECTROSCOPY

Citation Formats


                    Karmakar, P K, and Dwivedi, C B. Analytical integrability and physical solutions of d-KdV equation.  United States: N. p., 2006. 
        Web.  doi:10.1063/1.2173087.

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                    Karmakar, P K, & Dwivedi, C B. Analytical integrability and physical solutions of d-KdV equation.  United States.  https://doi.org/10.1063/1.2173087

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                    Karmakar, P K, and Dwivedi, C B. 2006.  
        "Analytical integrability and physical solutions of d-KdV equation".  United States.  https://doi.org/10.1063/1.2173087.

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@article{osti_20768741,

  title        = {Analytical integrability and physical solutions of d-KdV equation},

  author       = {Karmakar, P K and Dwivedi, C B},

  abstractNote = {A new idea of electron inertia-induced ion sound wave excitation for transonic plasma equilibrium has already been reported. In such unstable plasma equilibrium, a linear source driven Korteweg-de Vries (d-KdV) equation describes the nonlinear ion sound wave propagation behavior. By numerical techniques, two distinct classes of solution (soliton and oscillatory shocklike structures) are obtained. Present contribution deals with the systematic methodological efforts to find out its (d-KdV) analytical solutions. As a first step, we apply the Painleve method to test whether the derived d-KdV equation is analytically integrable or not. We find that the derived d-KdV equation is indeed analytically integrable since it satisfies Painleve property. Hirota's bilinearization method and the modified sine-Gordon method (also termed as sine-cosine method) are used to derive the analytical results. Perturbative technique is also applied to find out quasistationary solutions. A few graphical plots are provided to offer a glimpse of the structural profiles obtained by different methods applied. It is conjectured that these solutions may open a new scope of acoustic spectroscopy in plasma hydrodynamics.},

  doi          = {10.1063/1.2173087},

  url          = {https://www.osti.gov/biblio/20768741},
  journal      = {Journal of Mathematical Physics},

  issn         = {0022-2488},

  number       = 3,

  volume       = 47,

  place        = {United States},

  year         = {Wed Mar 15 00:00:00 EST 2006},

  month        = {Wed Mar 15 00:00:00 EST 2006}

}

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