A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws

Abstract In this study, we investigate a new fourth-order integrable nonlinear equation. Firstly, by means of the efficient Hirota bilinear approach, we establish novel types of solutions which include breather, rogue, and three-wave solutions. Secondly, with the aid of Lie symmetry method, we repor...

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Main Authors:	Dumitru Baleanu, Ali Saleh Alshomrani, Malik Zaka Ullah
Format:	Article
Language:	English
Published:	SpringerOpen 2021-04-01
Series:	Advances in Difference Equations
Subjects:	Fourth-order integrable nonlinear equation Lump solutions Interaction solutions Invariant analysis Conservation laws
Online Access:	https://doi.org/10.1186/s13662-021-03352-6

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spelling	doaj-8d5cc0a0b3aa4967a1a76da54907ba482021-04-11T11:38:03ZengSpringerOpenAdvances in Difference Equations1687-18472021-04-012021111610.1186/s13662-021-03352-6A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation lawsDumitru Baleanu0Ali Saleh Alshomrani1Malik Zaka Ullah2Department of Mathematics, Cankaya UniversityMathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, Faculty of Science, King Abdulaziz UniversityMathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, Faculty of Science, King Abdulaziz UniversityAbstract In this study, we investigate a new fourth-order integrable nonlinear equation. Firstly, by means of the efficient Hirota bilinear approach, we establish novel types of solutions which include breather, rogue, and three-wave solutions. Secondly, with the aid of Lie symmetry method, we report the invariance properties of the studied equation such as the group of transformations, commutator and adjoint representation tables. A differential substitution is found by nonlinear self-adjointness (NSA) and thereafter the associated conservation laws are established. We show some dynamical characteristics of the obtained solutions through via the 3-dimensional and contour graphs.https://doi.org/10.1186/s13662-021-03352-6Fourth-order integrable nonlinear equationLump solutionsInteraction solutionsInvariant analysisConservation laws
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Dumitru Baleanu Ali Saleh Alshomrani Malik Zaka Ullah
spellingShingle	Dumitru Baleanu Ali Saleh Alshomrani Malik Zaka Ullah A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws Advances in Difference Equations Fourth-order integrable nonlinear equation Lump solutions Interaction solutions Invariant analysis Conservation laws
author_facet	Dumitru Baleanu Ali Saleh Alshomrani Malik Zaka Ullah
author_sort	Dumitru Baleanu
title	A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws
title_short	A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws
title_full	A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws
title_fullStr	A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws
title_full_unstemmed	A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws
title_sort	new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2021-04-01
description	Abstract In this study, we investigate a new fourth-order integrable nonlinear equation. Firstly, by means of the efficient Hirota bilinear approach, we establish novel types of solutions which include breather, rogue, and three-wave solutions. Secondly, with the aid of Lie symmetry method, we report the invariance properties of the studied equation such as the group of transformations, commutator and adjoint representation tables. A differential substitution is found by nonlinear self-adjointness (NSA) and thereafter the associated conservation laws are established. We show some dynamical characteristics of the obtained solutions through via the 3-dimensional and contour graphs.
topic	Fourth-order integrable nonlinear equation Lump solutions Interaction solutions Invariant analysis Conservation laws
url	https://doi.org/10.1186/s13662-021-03352-6
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A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws

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