Multiple rogue wave solutions of the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation

Abstract

In this paper, a modified symbolic computation approach is proposed. The multiple rogue wave solutions of a generalized (2+1)-dimensional Boussinesq equation are obtained by using the modified symbolic computation approach. Dynamics features of these obtained multiple rogue wave solutions are displayed in 3D and contour plots. Compared with the original symbolic computation approach, our method does not need to find Hirota bilinear form of nonlinear system.

Localized nonlinear waves on spatio-temporally controllable backgrounds for a (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq model in water waves

“…The previously reported solutions of (3+1)D KPB model in Refs. [46][47][48][49][50][51][52][53][54], especially the soliton solutions [46] and rogue waves [48,54] obtained through Hirota bilinear formalism does not have any varying background. However, such controllable background in the present work offered much freedom to manipulate the nonlinear waves accordingly and displayed diverse wave phenomena.…”

“…However, the considered model ensures the Hirota bilinear form and so various physically interesting nonlinear wave structures. Looking at the literature on the KPB model (1), we can find that the solutions of one-and two-solitons using the simplified Hirota method [46], traveling waves using bilinear Bäcklund transformations [47], high-order breathers and rogue waves [48] and higher-order rogue waves with generalized polynomials [49] and lump and interaction waves [50] through Hirota's bilinear method are reported. Also, the Painlevé integrability analysis [51], localized wave solutions using bilinear form [52] and the symmetry reductions along with conserved quantities are obtained [53].…”

“…For further detailed analysis and discussion, one can refer to these reports and references therein. Note that the solutions reported in the above-mentioned works [46][47][48][49][50][51][52][53][54], especially the soliton and rogue wave solutions reported in [46,48,54], are on constant (zero/non-zero) background, while the solutions we intend to discuss here is on variable backgrounds. Considering the limited works for localized waves on variable backgrounds in higher-dimensional models, especially no such report is available for the present KPB model (1), we proceed to pursue our interest to construct localized nonlinear wave solutions on spatio-temporally controllable backgrounds and study their dynamics in detail.…”

Higher-order rogue waves with controllable fission and asymmetry localized in a (3 + 1)-dimensional generalized Boussinesq equation

“…More recently, some researchers [20][21][22][23][24][25][26][27] have focused on studying rogue wave solutions, especially higher-order rogue wave solutions of (3 + 1)-dimensional nonlinear models. In 2018, Zhaqilao [22] proposed the so-called symbolic computation approach to constructing rogue wave solutions with controllable centers of two high-dimensional nonlinear systems.…”

Variable-coefficient symbolic computation approach for finding multiple rogue wave solutions of nonlinear system with variable coefficients

“…Recently, a symbolic computation approach to obtain the multiple rogue wave solutions is proposed by Zhaqilao [15]. But the main application of this method is constant-coefficient integrable equation [16][17][18], which is not suitable for variable-coefficient integrable equation. So, we give an improved method named variable-coefficient symbolic computation approach (vcsca) to solve this problem and apply this method to Eq.…”