Journal ArticleDOI
Bäcklund transformation, Pfaffian, Wronskian and Grammian solutions to the (3 +1 ) -dimensional generalized Kadomtsev-Petviashvili equation
Xue-Jiao He,Xing Lü,Meng-Gang Li +2 more
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TLDR
In this article, the Hirota bilinear method and symbolic computation were used to construct the bilinearly Backlund transformation for the generalized Kadomtsev-Petviashvili equation.Abstract:
With the Hirota bilinear method and symbolic computation, we investigate the $$(3+1)$$
-dimensional generalized Kadomtsev–Petviashvili equation. Based on its bilinear form, the bilinear Backlund transformation is constructed, which consists of four equations and five free parameters. The Pfaffian, Wronskian and Grammian form solutions are derived by using the properties of determinant. As an example, the one-, two- and three-soliton solutions are constructed in the context of the Pfaffian, Wronskian and Grammian forms. Moreover, the triangle function solutions are given based on the Pfaffian form solution. A few particular solutions are plotted by choosing the appropriate parameters.read more
Citations
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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
New general interaction solutions to the KPI equation via an optional decoupling condition approach
Xing Lü,Si-Jia Chen +1 more
TL;DR: In this paper, an optional decoupling condition approach is proposed for deriving the lump-stripe solutions and lump-soliton solutions to the KPI equation, which can be applied to a wide class of nonlinear evolution equations.
Journal ArticleDOI
Derivation and simulation of the M-lump solutions to two (2+1)-dimensional nonlinear equations
TL;DR: In this article, the N-rational solutions to two (2+1)-dimensional nonlinear evolution equations are constructed by utilizing the long wave limit method, where 1-, 2-and 3-lump solutions are derived by making some parameters conjugate to each other.
Journal ArticleDOI
Bäcklund transformation, exact solutions and diverse interaction phenomena to a (3+1)-dimensional nonlinear evolution equation
Yu-Hang Yin,Xing Lü,Wen-Xiu Ma +2 more
TL;DR: In this paper, a bilinear Backlund transformation was used to construct a (3+1)-dimensional nonlinear evolution equation, which was proposed and analyzed to study features and properties of nonlinear dynamics in higher dimensions.
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
Linear superposition principle applying to Hirota bilinear equations
Wen-Xiu Ma,En-Gui Fan +1 more
TL;DR: A linear superposition principle of exponential traveled 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.
Journal ArticleDOI
Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation
Xing Lü,Wen-Xiu Ma,Wen-Xiu Ma +2 more
TL;DR: In this article, two classes of lump solutions to the dimensionally reduced equations in (2+1)-dimensions are derived, respectively, by searching for positive quadratic function solutions to associated bilinear equations.
Journal ArticleDOI
Constructing lump solutions to a generalized Kadomtsev–Petviashvili–Boussinesq equation
TL;DR: In this paper, a combined model of generalized bilinear Kadomtsev-Petviashvili and Boussinesq equation (gbKPB for short) in terms of the function f is proposed, which involves four arbitrary coefficients.
Journal ArticleDOI
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.
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Bäcklund transformation, exact solutions and interaction behaviour of the (3+1)-dimensional Hirota-Satsuma-Ito-like equation
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Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation
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