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

Advances in Difference Equations

Dumitru Baleanu¹  Malik Zaka Ullah²  Ali Saleh Alshomrani² 

[1] Department of Mathematics, Cankaya University, 06530, Ankara, Turkey;Institute of Space Sciences, Bucharest, Romania;Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, Faculty of Science, King Abdulaziz University, 21589, Jeddah, Saudi Arabia;

关键词: Fourth-order integrable nonlinear equation;    Lump solutions;    Interaction solutions;    Invariant analysis;    Conservation laws;   

DOI  :  10.1186/s13662-021-03352-6

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY