Qualitative study of effects of vorticity on traveling wave solutions to the two-component Zakharov–Itō system

Abstract

In this paper, we qualitatively study effects of vorticity on traveling wave solutions to the two-component Zakharov–Itō system from the perspective of dynamical systems and show that the vorticity $\mathrm{\Omega }=2c$ (c is the wave speed) is the critical vorticity. Based on this critical vorticity, we obtain all possible phase portraits of the system under exact explicit parameter conditions. Then we not only show the existence of all bounded traveling wave solutions including solitary wave solutions, periodic wave solutions, kinklike (antikink) wave solutions and compactons, under corresponding exact explicit parameter conditions, but also obtain the exact expressions of solitary wave solutions and blow-up solutions (unbounded solutions). The previous results are extended.

COMMUNICATED BY:

• A. Constantin

Keywords:

• Two-component Zakharov–Itō system
• vorticity
• traveling wave solutions
• bifurcation
• exact explicit parameter conditions

2010 Mathematics Subject Classifications:

• Primary: 34C60
• 35B32
• 35C07
• Secondary:34C37

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

The first author is supported by the National Natural Science Foundation of China (no. 11701191), Program for Innovative Research Team in Science and Technology in Fujian Province University, and Quanzhou High-Level Talents Support Plan under grant 2017ZT012.