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

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 inv...

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Bibliographic Details
Published in:Advances in difference equations 2021-04, Vol.2021 (1), p.1-16, Article 195
Main Authors: Baleanu, Dumitru, Alshomrani, Ali Saleh, Ullah, Malik Zaka
Format: Article
Language:English
Subjects:
Analysis
Commutators
Conservation laws
Difference and Functional Equations
Fourth-order integrable nonlinear equation
Functional Analysis
Interaction solutions
Invariant analysis
Lump solutions
Mathematics
Mathematics and Statistics
Nonlinear equations
Ordinary Differential Equations
Partial Differential Equations
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Summary: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.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-021-03352-6