Affiliation:
1. School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Abstract
The [Formula: see text]-dimensional Boussinesq equation plays a key role in modeling the shallow water. In this work, we derive a new fractional [Formula: see text]-dimensional Boussinesq equation based on the conformable fractional derivative for the first time. By means of the Hirota bilinear method, we obtain the [Formula: see text]-soliton, breather and lump solutions. In addition, the abundant traveling wave solutions like bright solitary, dark solitary wave solutions are investigated by applying the variational method. The solutions are presented through the 3D plots and 2D contours by assigning the proper parameters. The corresponding physical interpretations are also elaborated. The findings in this work are expected to open some new horizons on the study of fractional PDEs in physics.
Funder
Program of Henan Polytechnic University
Innovative Scientists and Technicians Team of Henan Provincial High Education
Fundamental Research Funds for the Universities of Henan Province
Key Project of Scientific and Technology Research of Henan Province
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Geometry and Topology,Modeling and Simulation
Cited by
20 articles.
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