Journal ArticleDOI
Lump, soliton, and interaction solutions to a generalized two-mode higher-order nonlinear evolution equation in plasma physics
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This article is published in Nonlinear Dynamics.The article was published on 2022-07-02. It has received 30 citations till now. The article focuses on the topics: Korteweg–de Vries equation & Soliton.read more
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N-fold Darboux transformation and solitonic interactions for the Kraenkel–Manna–Merle system in a saturated ferromagnetic material
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Bilinear form and Pfaffian solutions for a (2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt system in fluid mechanics and plasma physics
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Rogue-wave, rational and semi-rational solutions for a generalized (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation in a two-layer fluid
Feiyan Liu,Yi-Tian Gao,Xin Yu +2 more
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Analysis of interaction of lump solutions with kink-soliton solutions of the generalized perturbed KdV equation using Hirota-bilinear approach
TL;DR: Using the Hirota bilinear method (HBM) and Cole-Hopf transformation, this paper extracted the interaction between the lump and kink-soliton solutions for the generalized perturbed Korteweg-de Vries (KdV) equation.
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Wronskian solutions and Pfaffianization for a(3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili equation in a fluid or plasma
TL;DR: In this paper , a generalized variable-coefficient Kadomtsev-Petviashvili (GVCKP) equation in a fluid or plasma is investigated and the Nth-order Wronskian solutions for that equation are derived and proved under certain variable-efficient constraints, where N is a positive integer.
References
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The painleve property for partial differential equations. ii. backlund transformation, lax pairs, and the schwarzian derivative
TL;DR: In this article, the authors investigated the Painleve property for partial differential equations and showed that it is invariant under the Moebius group (acting on dependent variables) and obtained the appropriate Lax pair for the underlying nonlinear pde.
The Direct Method In Soliton Theory
TL;DR: The the direct method in soliton theory is universally compatible with any devices to read, and is available in the book collection an online access to it is set as public so you can download it instantly.
Journal ArticleDOI
The Hirota’s direct method for multiple-soliton solutions for three model equations of shallow water waves
TL;DR: The Hirota bilinear method is used to determine multiple-soliton solutions of sech-squared type for three model equations for shallow water waves that are completely integrable.
Journal ArticleDOI
Bilinear auto-Bäcklund transformations and soliton solutions of a (3+1)-dimensional generalized nonlinear evolution equation for the shallow water waves
Yuan Shen,Bo Tian +1 more
TL;DR: Three bilinear auto-Backlund transformations are presented based on the Hirota method for the shallow water waves, along with some soliton solutions that depend on the water-wave coefficients in that equation.
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Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation
Runfa Zhang,Sudao Bilige +1 more
TL;DR: In this article, a new method named bilinear neural network is introduced, and the corresponding tensor formula is proposed to obtain the exact analytical solutions of nonlinear partial differential equations (PDEs).
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