Interaction dynamics of hybrid solitons and breathers for extended generalization of Vakhnenko equation

• Published in: Nonlinear dynamics Vol. 102; no. 3; pp. 1787 - 1799
• Main Authors: Li, Bang-Qing, Ma, Yu-Lan
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.11.2020; Springer Nature B.V
• Subjects: Automotive Engineering; Breathers; Classical Mechanics; Complex numbers; Control; Dynamical Systems; Elastic scattering; Engineering; Mechanical Engineering; Original Paper; Solitary waves; Vibration; Hirota bilinear method; General; Extended generalization of Vakhnenko equation (EGVE); Interactions dynamics; Loop-like soliton; order auxiliary function; Loop-like breather
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-020-06024-4

The main attention of this study is focused on the interaction dynamics of breather, and hybrid solitons and breather for an extended generalization of Vakhnenko equation. The general form of the N -order auxiliary function is first derived by the Hirota bilinear method. Then, the N -order solutions can be obtained. When N ≥ 2 , the loop-like breather may emerge by taking the dispersion coefficients as conjugate complex number. The breather is like a magical spring with good elasticity, changeable period and thickness. Furthermore, novel interaction features between breathers, between soliton/solitons and breather/breathers, are observed by visualizing method. The results show that there are abundant dynamics during the interactions, such as elastic collision, phase shift, amplitude amplification, collapse and bulge effect.