Journal ArticleDOI
Lump and lump-soliton solutions to the $$(2+1)$$ ( 2 + 1 ) -dimensional Ito equation
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Based on the Hirota bilinear form of the $$(2+1)$$ -dimensional Ito equation, one class of lump solutions and two classes of interaction solutions between lumps and line solitons are generated through analysis and symbolic computations with Maple.Abstract:
Based on the Hirota bilinear form of the $$(2+1)$$
-dimensional Ito equation, one class of lump solutions and two classes of interaction solutions between lumps and line solitons are generated through analysis and symbolic computations with Maple. Analyticity is naturally guaranteed for the presented lump and interaction solutions, and the interaction solutions reduce to lumps (or line solitons) while the hyperbolic-cosine (or the quadratic function) disappears. Three-dimensional plots and contour plots are made for two specific examples of the resulting interaction solutions.read more
Citations
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Abundant lumps and their interaction solutions of (3+1)-dimensional linear PDEs
TL;DR: In this article, the existence of diverse lump and interaction solutions to linear partial differential equations in (3+1)-dimensions was explored through Maple symbolic computations, which yields exact lump, lump-periodic and lump-soliton solutions.
Journal ArticleDOI
Interaction solutions to Hirota-Satsuma-Ito equation in (2 + 1)-dimensions
TL;DR: In this paper, exact interaction solutions, including lump-soliton, lump-kink, and lumpperiodic solutions, are computed for Hirota-Satsuma-Ito equation in (2 + 1)-dimensions, through conducting symbolic computations with Maple.
Journal ArticleDOI
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).
Journal ArticleDOI
Lump solutions to a generalized Bogoyavlensky-Konopelchenko equation
TL;DR: In this paper, a (2 + 1)-dimensional generalized Bogoyavlensky-Konopelchenko equation that possesses a Hirota bilinear form is considered, and a class of explicit lump solutions is computed through conducting symbolic computations with Maple, and some plots of a specic presenteded lump solution are made to shed light on the characteristics of lumps.
Journal ArticleDOI
Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions
TL;DR: The fractional order model can open up a new window for better understanding the waves in fluid and help comprehending generalization and evolution of Rossby solitary waves in stratified fluid.
References
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Book
Solitons, Nonlinear Evolution Equations and Inverse Scattering
M. A. Ablowitz,Peter A. Clarkson +1 more
TL;DR: In this article, the authors bring together several aspects of soliton theory currently only available in research papers, including inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multidimensional space, and the ∂ method.
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.
Book ChapterDOI
Solitons, Nonlinear Evolution Equations and Inverse Scattering: References
M. A. Ablowitz,Peter A. Clarkson +1 more
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.
Journal ArticleDOI
Two‐dimensional lumps in nonlinear dispersive systems
TL;DR: In this article, two-dimensional lump solutions which decay to a uniform state in all directions are obtained for the Kadomtsev-Petviashvili and Schrodinger type equation.