Lump solutions to the ($$\mathbf 2+1 $$2+1)-dimensional Sawada–Kotera equation
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DOI: 10.1007/s11071-016-3190-6
Abstract: In this paper, via generalized bilinear forms, we consider the ($$2+1$$2+1)-dimensional bilinear p-Sawada–Kotera (SK) equation. We derive analytical rational solutions in terms of positive quadratic functions. Through applying the dependent transformation, we present a class… read more here.
Keywords: sawada kotera; lump; lump solutions; equation ... See more keywords
Bäcklund transformation, multiple wave solutions and lump solutions to a (3 + 1)-dimensional nonlinear evolution equation
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DOI: 10.1007/s11071-017-3581-3
Abstract: In this paper, a $$(3+1)$$(3+1)-dimensional nonlinear evolution equation is cast into Hirota bilinear form with a dependent variable transformation. A bilinear Bäcklund transformation is then presented, which consists of six bilinear equations and involves nine… read more here.
Keywords: nonlinear evolution; wave solutions; transformation; dimensional nonlinear ... See more keywords
Localized solutions of (5+1)-dimensional evolution equations
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DOI: 10.1007/s11071-021-06541-w
Abstract: In this research, the general linear evolution equations (EEs) in (5+1) dimensions are studied. All the mixed second-order derivatives are included in this aforementioned model. Using the Hirota bilinear operator and symbolic computation, the localized… read more here.
Keywords: solutions dimensional; localized solutions; abundant lump; lump solutions ... See more keywords
New interaction of high-order breather solutions, lump solutions and mixed solutions for (3+1)-dimensional Hirota–Satsuma–Ito-like equation
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DOI: 10.1007/s11071-021-06895-1
Abstract: Under investigation in this letter is an (3+1)-dimensional Hirota–Satsuma–Ito-like equation, which provide strong support for studying the dynamic behavior of nonlinear waves. Based on a special Cole–Hopf transformation and Hirota bilinear method, the bilinear form… read more here.
Keywords: solutions lump; order breather; lump solutions; equation ... See more keywords
General lump solutions, lumpoff solutions, and rogue wave solutions with predictability for the (2+1)-dimensional Korteweg-de Vries equation
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DOI: 10.1007/s40314-019-0938-x
Abstract: In this work, the (2+1)-dimensional Korteweg-de Vries equation is investigated, which can be used to represent the amplitude of the shallow–water waves in fluids or electrostatic wave potential in plasmas. By employing the properties of… read more here.
Keywords: lumpoff solutions; dimensional korteweg; korteweg vries; vries equation ... See more keywords
From 2Mth-order wronskian determinant solutions to Mth-order lump solutions for the (2+1)-Dimensional Kadomtsev–Petviashvili I equation
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DOI: 10.1016/j.wavemoti.2021.102746
Abstract: Abstract In this paper, the Mth-order lump solutions for the (2+1)-dimensional Kadomtsev–Petviashvili I equation are studied. Firstly, the Nth-order wronskian determinant solutions of the Hirota bilinear form of the (2+1)-dimensional Kadomtsev–Petviashvili I equation are given.… read more here.
Keywords: order lump; order; lump solutions; wronskian determinant ... See more keywords
Dynamical analysis of lump solutions for (3 + 1) dimensional generalized KP–Boussinesq equation and Its dimensionally reduced equations
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DOI: 10.1088/1402-4896/aac8b8
Abstract: This paper analyzes a new form of the (3 + 1) dimensional generalized Kadomtsev–Petviashvili (KP)–Boussinesq equation for exploring lump solutions by making use of its Hirota bilinear form. The sufficient and necessary conditions for assuring… read more here.
Keywords: generalized boussinesq; boussinesq equation; dimensional generalized; dimensionally reduced ... See more keywords
Derivation and simulation of the M-lump solutions to two (2+1)-dimensional nonlinear equations
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DOI: 10.1088/1402-4896/abf307
Abstract: The N-rational solutions to two (2+1)-dimensional nonlinear evolution equations are constructed by utilizing the long wave limit method. M-lump solutions to the two equations are derived by making some parameters conjugate to each other. We… read more here.
Keywords: multiple lump; solutions two; two dimensional; lump ... See more keywords
Lump solutions with interaction phenomena in the (2+1)-dimensional Ito equation
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DOI: 10.1142/s021798491850104x
Abstract: In this paper, we consider the (2+1)-dimensional Ito equation, which was introduced by Ito. By considering the Hirota’s bilinear method, and using the positive quadratic function, we obtain some lu... read more here.
Keywords: lump solutions; solutions interaction; ito equation; dimensional ito ... See more keywords
Lump solutions to a (2+1)-dimensional fourth-order nonlinear PDE possessing a Hirota bilinear form
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DOI: 10.1142/s0217984921501608
Abstract: Wen-Xiu Ma∗,†,‡,§,∗∗, Solomon Manukure¶, Hui Wang‡,‖ and Sumayah Batwa†,‡ ∗Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China †Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia ‡Department of Mathematics and Statistics, University… read more here.
Keywords: solutions dimensional; department mathematics; lump solutions; mathematics ... See more keywords