On the Solutions of a $$2+1$$2+1-Dimensional Model for Epitaxial Growth with Axial Symmetry
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DOI: 10.1007/s00332-017-9428-8
Abstract: In this paper, we study the evolution equation derived by Xu and Xiang (SIAM J Appl Math 69(5):1393–1414, 2009) to describe heteroepitaxial growth in $$2+1$$2+1 dimensions with elastic forces on vicinal surfaces is in the… read more here.
Keywords: epitaxial growth; dimensional model; model epitaxial; growth axial ... See more keywords
On Lie symmetries and soliton solutions of $$(2+1)$$(2+1)-dimensional Bogoyavlenskii equations
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DOI: 10.1007/s11071-018-4509-2
Abstract: The present article is devoted to find some invariant solutions of the $$(2+1)$$(2+1)-dimensional Bogoyavlenskii equations using similarity transformations method. The system describes $$(2+1)$$(2+1)-dimensional interaction of a Riemann wave propagating along y-axis with a long wave… read more here.
Keywords: lie symmetries; bogoyavlenskii equations; soliton solutions; dimensional bogoyavlenskii ... 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
Dynamic properties of interactional solutions for the (4 + 1)-dimensional Fokas equation
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DOI: 10.1007/s11071-021-06789-2
Abstract: In this paper, based on the bilinear form, we give multi-solitary wave solutions of the $$(4+1)$$ -dimensional Fokas equation. From the obtained multi-solitary wave solutions, with special parameters, we derive resonant solutions of N-solitary waves.… read more here.
Keywords: dynamic properties; solitary wave; fokas equation; solutions dimensional ... See more keywords
New analytical solutions of (2 + 1)-dimensional conformable time fractional Zoomeron equation via two distinct techniques
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DOI: 10.1016/j.cjph.2018.09.013
Abstract: Abstract In this paper, the new exact solutions for the (2 + 1) dimensional time fractional Zoomeron equation have been derived via two efficient analytical techniques, which are the extended exp ( − Φ ( ξ )… read more here.
Keywords: time fractional; fractional zoomeron; via two; solutions dimensional ... See more keywords
Multiwave interaction solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation
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DOI: 10.1016/j.cjph.2021.03.001
Abstract: Abstract To construct a class of new multiwave interaction solutions for the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation, we calculate different types of interaction solutions among solitons, periodic waves and rational waves using the direct algebraic method… read more here.
Keywords: solutions dimensional; generalized kadomtsev; interaction solutions; kadomtsev petviashvili ... See more keywords
Periodic solutions for an N-dimensional cyclic feedback system with delay
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DOI: 10.1016/j.jde.2019.11.028
Abstract: Abstract We study models for N cyclically coupled variables (e.g., neuron activities) with overall negative delayed feedback, and without symmetry or monotonicity properties. Our aim is to extract the common parts of similar approaches that… read more here.
Keywords: periodic solutions; cyclic feedback; feedback; feedback system ... See more keywords
Analytical wave solutions of the (2 + 1)-dimensional first integro-differential Kadomtsev-Petviashivili hierarchy equation by using modified mathematical methods
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DOI: 10.1016/j.rinp.2019.102775
Abstract: Abstract In our research, we ascertain abundant novel exact traveling wave solutions of (2 + 1)-dimensional first integro-differential Kadomtsev-Petviashivili hierarchy equation by two new modified mathematical methods namely called generalized direct algebraic and extended simple equation methods… read more here.
Keywords: integro differential; wave solutions; solutions dimensional; dimensional first ... See more keywords
Resonant multi-soliton and multiple rogue wave solutions of (3+1)-dimensional Kudryashov-Sinelshchikov equation
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DOI: 10.1088/1402-4896/ac098b
Abstract: In this paper, we investigated various exact solutions of (3+1)-dimensional Kudryashov-Sinelshchikov equation in a mixture of liquid and gas bubbles. At first, the linear superposition principle was introduced to obtain resonant multi-soliton solutions and we… read more here.
Keywords: sinelshchikov equation; dimensional kudryashov; wave solutions; kudryashov sinelshchikov ... See more keywords
Analytic topologically nontrivial solutions of the (3+1)-dimensional $U(1)$ gauged Skyrme model and extended duality
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DOI: 10.1103/physrevd.96.125005
Abstract: We construct the first analytic examples of topologically non-trivial solutions of the (3+1)-dimensional $U(1)$ gauged Skyrme model within a finite box in (3+1)-dimensional flat space-time. There are two types of gauged solitons. The first type… read more here.
Keywords: time; gauged skyrme; solutions dimensional; skyrme model ... See more keywords
M-lump and interaction solutions of a ($$2+1$$)-dimensional extended shallow water wave equation
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DOI: 10.1140/epjp/s13360-021-01188-3
Abstract: In this paper, a more extended ( $$2+1$$ )-dimensional shallow water wave equation is considered, which is integrable in terms of the Hirota’s bilinear method. With the aid of the bilinear method, the N-soliton solutions… read more here.
Keywords: solutions dimensional; water; water wave; interaction solutions ... See more keywords