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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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2021

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Baleanu, Dumitru
Alshomrani, Ali Saleh
Ullah, Malik Zaka

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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.

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Fourth-Order Integrable Nonlinear Equation, Lump Solutions, Interaction Solutions, Invariant Analysis, Conservation Laws

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Baleanu, Dumitru; Alshomrani, Ali Saleh; Ullah, Malik Zaka (2021). "A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws", Advances in Difference Equations, Vol. 2021, No. 1.

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Advances in Difference Equations

Volume

2021

Issue

1

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