Qualitative study of effects of vorticity on traveling wave solutions to the two-component Zakharov–Itō system. Issue 11 (18th August 2021)

• Record Type: Journal Article
• Authors: Wen, Zhenshu
• Is Part Of: Applicable analysis. Volume 100:Issue 11(2021)
• Page Start: 2334
• Page End: 2346
• Publication Date: 2021-08-18
• Subjects: A. Constantin; Two-component Zakharov–Itō system -- vorticity -- traveling wave solutions -- bifurcation -- exact explicit parameter conditions; Primary: 34C60 -- 35B32 -- 35C07 -- Secondary:34C37; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1680831
• Languages: English
• ISSNs: 0003-6811

Abstract

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 Ω = 2 c ( 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.