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Rational and Semirational Solutions of the Nonlocal Davey–Stewartson Equations
Author(s) -
Rao J.,
Cheng Y.,
He J.
Publication year - 2017
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12178
Subject(s) - breather , invertible matrix , constant (computer programming) , mathematical analysis , line (geometry) , mathematics , rogue wave , bilinear interpolation , physics , mathematical physics , classical mechanics , nonlinear system , pure mathematics , geometry , quantum mechanics , statistics , computer science , programming language
In this paper, the partially party‐time ( P T ) symmetric nonlocal Davey–Stewartson (DS) equations with respect to x is called x ‐nonlocal DS equations, while a fully P T symmetric nonlocal DSII equation is called nonlocal DSII equation. Three kinds of solutions, namely, breather, rational, and semirational solutions for these nonlocal DS equations are derived by employing the bilinear method. For the x ‐nonlocal DS equations, the usual (2 + 1)‐dimensional breathers are periodic in x direction and localized in y direction. Nonsingular rational solutions are lumps, and semirational solutions are composed of lumps, breathers, and periodic line waves. For the nonlocal DSII equation, line breathers are periodic in both x and y directions with parallels in profile, but localized in time. Nonsingular rational solutions are (2 + 1)‐dimensional line rogue waves, which arise from a constant background and disappear into the same constant background, and this process only lasts for a short period of time. Semirational solutions describe interactions of line rogue waves and periodic line waves.