Journal ArticleDOI
Abundant exact solutions and interaction phenomena of the (2 + 1)-dimensional YTSF equation
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TLDR
In this paper, the Hirota bilinear formulation of the (2 + 1)-dimensional Yu-Toda-Sasa-Fukuyama equation is used to generate exact solutions including the lump and interaction solutions.Abstract:
In this paper, we study abundant exact solutions including the lump and interaction solutions to the (2 + 1)-dimensional Yu–Toda–Sasa–Fukuyama equation. With symbolic computation, lump solutions and the interaction solutions are generated directly based on the Hirota bilinear formulation. Analyticity and well-definedness is guaranteed through some conditions posed on the parameters. With special choices of the involved parameters, the interaction phenomena are simulated and discussed. We find the lump moves from one hump to the other hump of the two-soliton, while the lump separates from the hump of the one-soliton.read more
Citations
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Bäcklund transformation, exact solutions and interaction behaviour of the (3+1)-dimensional Hirota-Satsuma-Ito-like equation
Si-Jia Chen,Wen-Xiu Ma,Xing Lü +2 more
TL;DR: A (3+1)-dimensional Hirota-Satsuma-Ito-like equation is introduced based on the (2+1), and Backlund transformation and corresponding exponential function solutions are deduced by virtue of the Hirota bilinear form.
Journal ArticleDOI
Interaction solutions to nonlinear partial differential equations via Hirota bilinear forms: one-lump-multi-stripe and one-lump-multi-soliton types
Xing Lü,Si-Jia Chen +1 more
TL;DR: In this article, the authors analyzed the one-lump-multi-stripe and soliton solutions to nonlinear partial differential equations via Hirota bilinear forms and provided necessary and sufficient conditions for the two types of interaction solutions, respectively.
Journal ArticleDOI
Integrability characteristics of a novel (2+1)-dimensional nonlinear model: Painlevé analysis, soliton solutions, Bäcklund transformation, Lax pair and infinitely many conservation laws
TL;DR: This paper conducts the Painleve analysis of the novel (2+1)-dimensional Kadomtsev-Petviashvili type equations and derives the soliton solutions and gives the formula of the N -soliton solution, which is proved by means of the Hirota condition.
Journal ArticleDOI
Localized characteristics of lump and interaction solutions to two extended Jimbo-Miwa equations
Yu-Hang Yin,Si-Jia Chen,Xing Lü +2 more
Journal ArticleDOI
Conserved quantities along with Painlevé analysis and optical solitons for the nonlinear dynamics of Heisenberg ferromagnetic spin chains model
TL;DR: In this paper, the authors investigated a famous model of nonlinear sciences namely (2 + 1)-dimensional nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) model for the evaluation of the (1 − 1)-approximation.
References
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Book
The direct method in soliton theory
TL;DR: In this paper, Bilinearization of soliton equations is discussed and the Backlund transformation is used to transform the soliton equation into a linear combination of determinants and pfaffians.
Journal ArticleDOI
Lump solutions to the Kadomtsev–Petviashvili equation
TL;DR: In this article, a class of lump solutions, rationally localized in all directions in the space, to the (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation is presented, making use of its Hirota bilinear form.
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Two-dimensional solitons of the Kadomtsev-Petviashvili equation and their interaction
TL;DR: In this article, it was shown that two-dimensional solitons do not interact at all, unlike one-dimensional ones, and explicit analytic formulae for 2D solitions are given.
Journal ArticleDOI
Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation
TL;DR: In this paper, a detailed study of the inverse scattering transform of the non-local nonlinear Schrodinger (NLS) equation is carried out and key symmetries of the eigenfunctions and scattering data and conserved quantities are obtained.
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