Journal ArticleDOI
A New $$(3+1)$$ -dimensional Hirota Bilinear Equation: Its Bäcklund Transformation and Rational-type Solutions
TLDR
In this paper, the behavior of specific dispersive waves in a new 3D-HB equation is studied and a Backlund transformation and a Hirota bilinear form of the model are first extracted from the truncated Painleve expansion.Abstract:
The behavior of specific dispersive waves in a new $$(3+1)$$
-dimensional Hirota bilinear (3D-HB) equation is studied. A Backlund transformation and a Hirota bilinear form of the model are first extracted from the truncated Painleve expansion. Through a series of mathematical analyses, it is then revealed that the new 3D-HB equation possesses a series of rational-type solutions. The interaction of lump-type and 1-soliton solutions is studied and some interesting and useful results are presented.read more
Citations
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Extractions of some new travelling wave solutions to the conformable Date-Jimbo-Kashiwara-Miwa equation
TL;DR: In this paper, complex and combined dark-bright characteristic properties of nonlinear Date-Jimbo-Kashiwara-Miwa equation with conformable are extracted by using two powerful analytical approaches.
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Dynamic behavior of the (3+1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff equation
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Study on dynamical behavior of multiple lump solutions and interaction between solitons and lump wave
TL;DR: In this article, a new (3+1)-dimensional Hirota bilinear equation in fluids is investigated and the interaction solutions of lump and N-soliton are obtained.
Journal ArticleDOI
Qualitative analysis of solutions for the p Laplacian hyperbolic equation with logarithmic nonlinearity
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Multi-solutions with specific geometrical wave structures to a nonlinear evolution equation in the presence of the linear superposition principle
TL;DR: In this article , the generalized Hietarintatype equation was investigated with multiple M-lump solutions and collision phenomena with soliton wave solutions, and the results expressed physical features of lump and lump interaction phenomena of different kinds of nonlinear physical processes.
References
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Journal ArticleDOI
Lump solutions to nonlinear partial differential equations via Hirota bilinear forms
Wen-Xiu Ma,Yuan Zhou +1 more
TL;DR: In this article, a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations are analyzed, based on the Hirota bilinear formulation and the primary object is the class of positive multivariate quadrastic functions.
Posted Content
Lump solutions to nonlinear partial differential equations via Hirota bilinear forms
Wen-Xiu Ma,Yuan Zhou +1 more
TL;DR: In this article, a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations are analyzed. But the basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadral functions.
Journal ArticleDOI
Diversity of interaction solutions to the (2+1)-dimensional Ito equation
TL;DR: The diversity of interaction solutions to the (2+1)-dimensional Ito equation, based on its Hirota bilinear form, is shown, which includes lump solutions, lump-soliton solutions and lump-kink solutions.
Journal ArticleDOI
Mixed lump-kink solutions to the BKP equation
TL;DR: By using the Hirota bilinear form of the (2+1)-dimensional BKP equation, ten classes of interaction solutions between lumps and kinks are constructed through Maple symbolic computations beginning with a linear combination ansatz.
Journal ArticleDOI
A search for bilinear equations passing Hirota's three-soliton condition. II. mKdV-type bilinear equations
TL;DR: In this paper, the results of a search for complex bilinear equations with two-soliton solutions are presented, and it is found that the existence of two-solomon solutions is not automatic, but introduces conditions that are like the usual three and four-solon conditions.