Soliton molecules and other diverse wave solutions of the (2 + 1)-dimensional Boussinesq equation for the shallow water

• Published in: European physical journal plus Vol. 138; no. 10; p. 891
• Main Author: Wang, Kang-Jia
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 07.10.2023; Springer Nature B.V
• Subjects: Applied and Technical Physics; Atomic; Boussinesq equations; Complex Systems; Condensed Matter Physics; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Physics; Physics and Astronomy; Regular Article; Shallow water; Solitary waves; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-023-04521-0

In the current study, we are mainly concerned with the (2 + 1)-dimensional Boussinesq equation (BE) that plays a major role in describing the shallow water. Firstly, the resonance conditions of the soliton molecules are explored based on the N-soliton solution that extracted via the Hirota bilinear method. Secondly, some new kinds of the different waves solutions including the bright solitary, dark solitary, bright-singular solitary, dark-singular solitary and singular periodic wave solutions are investigated by manipulating two effective methods namely, Wang’s direct mapping method-II(WDMM-II) and Sub-equation method (SEM). The dynamical behaviors of the soliton molecules on the planes such as the ( x , t ) , ( y , t ) and ( x , y ) as well as the other wave solutions are discussed by displaying some graphics. The methods adopted in this work are hopeful to give some new inspiration on the study of the other PDEs in physics.