N-SOLITON, BREATHER, LUMP SOLUTIONS AND DIVERSE TRAVELING WAVE SOLUTIONS OF THE FRACTIONAL (2 + 1)-DIMENSIONAL BOUSSINESQ EQUATION

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.