Symmetry solutions and conservation laws of a (3+1)-dimensional generalized KP-Boussinesq equation in fluid mechanics

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.…”

“…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]. Recently, Manafian has reported multi-rogue wave solutions using generalized polynomials and reduced bilinear form along with kink-soliton solutions using multiple exp-function method for the present KPB model [54].…”

“…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.…”

Symmetry and complexity: A Lie symmetry approach to bifurcation, chaos, stability and travelling wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili equation

“…Lie symmetry analysis [17] is concerned with identifying the transformations, or symmetries, that keep a given differential equation unchanged. These symmetries are often derived from infinitesimal operators called Lie operators, which form a Lie algebra.…”

“…In 2018, Jadaun and Kumar studied the symmetry analysis and invariant solutions of the generalized (3+1)-dimensional KP equation [16]. Moleleki et al [17] conducted a thorough investigation of the symmetry solutions and conservation laws pertaining to a (3+1)-dimensional generalized KP-Boussinesq equation in the field of fluid mechanics. Kumar et al [18] have undertaken a study concerning the Lie symmetries, optimal system, and group-invariant solutions of the generalized KP equation in (3+1) dimensions.…”