Auto-Backlund transformations, bilinear forms, multiple-soliton, quasi-soliton and hybrid solutions of a (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in an electron-positron plasma

Electron-positron plasmas appear in the early Universe and many cosmic environments. In this paper, a (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in an electron-positron plasma is studied. Based on the truncated Painleve expansion, auto-Backlund transformations are derived. Via the Hirota method, bilinear forms are derived. Based on the bilinear forms, multiple-soliton solutions are obtained. Via the two- and four-soliton solutions under the complex conjugated transformations, one- and two-quasi-soliton solutions are derived. Via the three-soliton solutions under the complex conjugated transformations, we obtain hybrid solutions composed of a soliton and a quasi-soliton wave. Via the asymptotic analysis, we derive that the interactions between these solitons are elastic.

Automated summary

In this paper, a (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in an electron-positron plasma is studied. Auto-Backlund transformations are derived based on the truncated Painleve expansion. Bilinear forms are derived using the Hirota method. Multiple-soliton solutions are obtained based on the bilinear forms. One- and two-quasi-soliton solutions are derived using the two- and four-soliton solutions under complex conjugate transformations. Hybrid solutions composed of a soliton and a quasi-soliton wave are obtained via three-soliton solutions under complex conjugate transformations. The interactions between these solitons are derived to be elastic through asymptotic analysis.