Multiple-order line rogue wave, lump and its interaction, periodic, and cross-kink solutions for the generalized CHKP equation

• Main Authors: Yufeng Qian, Jalil Manafian, Sherin Youns Mohyaldeen, Liqaa S. Esmail, Sergey Alekseevich Gorovoy, Gurpreet Singh
• Format: Article
• Language: English
• Published: Elsevier 2021-09-01
• Series: Propulsion and Power Research
• Subjects: Multiple rogue wave solutions; Multiple soliton solutions; Generalized Camassa-Holm-Kadomtsev-Petviashvili equation; Lump solution; Hirota operator
• Online Access: http://www.sciencedirect.com/science/article/pii/S2212540X21000407

The multiple-order line rogue wave solutions method is emp loyed for searching the multiple soliton solutions for the generalized (2 + 1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili (CHKP) equation, which contains first-order, second-order, and third-order waves solutions. At the critical point, the second-order derivative and Hessian matrix for only one point will be investigated and the lump solution has one minimum value. For the case, the lump solution will be shown the bright-dark lump structure and for another case can be present the dark lump structure-two small peaks and one deep hole. Also, the interaction of lump with periodic waves and the interaction between lump and soliton can be obtained by introducing the Hirota forms. In the meanwhile, the cross-kink wave and periodic wave solutions can be gained by the Hirota operator. The physical phenomena of these gained multiple soliton solutions are analyzed and indicated in figures by selecting suitable values. We alternative offer that the determining method is general, impressive, outspoken, and powerful and can be exerted to create exact solutions of various kinds of nonlinear models originated in mathematical physics and engineering.