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2011•Journal of Mathematical PhysicsRequires access

Bäcklund transformation, Lax pair, and solutions for the Caudrey–Dodd–Gibbon equation

Qi‐Xing Qu, Bo Tian, Kun Sun, Yan Jiang

Open publisher page 11 citations

Abstract

By using Bell polynomials and symbolic computation, we investigate the Caudrey–Dodd–Gibbon equation analytically. Through a generalization of Bells polynomials, its bilinear form is derived, based on which, the periodic wave solution and soliton solutions are presented. And the soliton solutions with graphic analysis are also given. Furthermore, Bäcklund transformation and Lax pair are derived via the Bells exponential polynomials. Finally, the Ablowitz-Kaup-Newell-Segur system is constructed.

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What this paper is about

By using Bell polynomials and symbolic computation, we investigate the Caudrey–Dodd–Gibbon equation analytically. Through a generalization of Bells polynomials, its bilinear form is derived, based on which, the periodic wave solution and soliton solutions are presented. And the soliton solutions with graphic analysis are also given. Furthermore, Bäcklund transformation and Lax pair are derived via the Bells exponential polynomials. Finally, the Ablowitz-Kaup-Newell-Segur system is constructed.

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OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

By using Bell polynomials and symbolic computation, we investigate the Caudrey–Dodd–Gibbon equation analytically. Through a generalization of Bells polynomials, its bilinear form is derived, based on which, the periodic wave solution and soliton solutions are presented. And the soliton solutions with graphic analysis are also given. Furthermore, Bäcklund transformation and Lax pair are derived via the Bells exponential polynomials. Finally, the Ablowitz-Kaup-Newell-Segur system is constructed.

Key concepts: Bell polynomials, Mathematics, Lax pair, Transformation (genetics), Symbolic computation, Generalization, Bilinear form, Bilinear interpolation

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