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

Yufeng Qian ^a,*, Jalil Manafian ^b,c,**, Sherin Youns Mohyaldeen ^d, Liqaa S. Esmail ^e, Sergey Alekseevich Gorovoy ^f, Gurpreet Singh ^g

a. School of Science, Hubei University of Technology, Wuhan, 430068, China
         b. Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
         c. Natural Sciences Faculty, Lankaran State University, 50, H. Aslanov str., Lankaran, Azerbaijan
         d. Business Administration Department, Zakho Technical Institute, Duhok Polytechnic University, Kurdistan Region, Iraq
         e. Pharmacy Department, Duhok Technical Institute, Duhok Ploytechnic University, Kurdistan Region, Iraq
         f. Department of Machine Repair and Materials Science, Kuban State Agrarian University named after I.T. Trubilin, Krasnodar, Russian Federation
         g. Department of Mathematics, Sant Baba Bhag Singh Universitiy, Jalandhar, 144030, India

Abstract: The multiple-order line rogue wave solutions method is employed 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.

Keywords: Multiple rogue wave solutions; Multiple soliton solutions; Generalized Camassa-Holm-Kadomtsev-Petviashvili equation; Lump solution; Hirota operator

https://doi.org/10.1016/j.jppr.2021.09.002