Lump, multi-lump, cross kinky-lump and manifold periodic-soliton solutions for the (2+1)-D Calogero–Bogoyavlenskii–Schiff equation

Abstract

A bilinear form of the (2þ1)-dimensional nonlinear Calogero-Bogoyavlenskii-Schiff (CBS) model is derived using a transformation of dependent variable, which contain a controlling parameter. This parameter can control the direction, wave height and angle of the traveling wave. Based on the Hirota bilinear form and ansatz functions, we build many types of novel structures and manifold periodic-soliton solutions to the CBS model. In particular, we obtain entirely exciting periodic-soliton, cross-kinky-lump wave, double kinky-lump wave, periodic cross-kinkylump wave, periodic two-solitary wave solutions as well as breather style of two-solitary wave solutions. We present their propagation features via changing the existence parametric values in graphically. In addition, we estimate a condition that the waves are propagated obliquely for η 6 ¼ 0 , and orthogonally for η ¼ 0.

On integrability of an extended Bogoyavlenskii‐Kadomtsev‐Petviashvili equation: Multiple soliton solutions

“…where u k (x, y, t) 0 s (k = 0,1,2, …) are the functions of x, y, and t. Substituting (7) in Equation 3, and following the Painlevé analysis, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] we obtain the characteristic equation with five resonances at k = −1, 1, 4, 5, and 6. The resonance at k = −1 is related to singular manifold ψ(x, y, t) = 0.…”

“…The construction of higher‐dimensional integrable equations plays a fundamental role in the theory of propagation of waves and integrable systems. Examples of higher‐dimensional integrable equations are the (2 + 1)‐dimensional KdV, KP, Boussinesq equations, and others 1‐10 . The integrable equations have been extensively investigated mathematically and physically in a vast number of scientific and engineering fields, such as plasma physics, solid state physics, fiber optics, propagation of waves, chemical physics, tsunami, and other fields 11‐22 .…”

“…For α ≠ 0, the equation is a modification of the CBS equation, also understood as a modification of the Kadomtsev-Petviashvili equation (KP). [1][2][3][4][5][6][7][8] This equation was derived in Reference 1 by a reduction of the well-known (3 + 1)dimensional KP equation. The BKP equation (1) describes the propagation of nonlinear waves in a variety of scientific fields such as plasmas, fluid dynamics, shallow waters waves, tsunami, and many others.…”

“…Many systematic powerful methods are used to study the nonlinear equations, integrable and nonintegrable. The generalized symmetry method, Painlevé analysis, the inverse scattering method, the Bäcklund transformation method, the conservation law method, the Cole-Hopf transformation, Bell polynomials method, tanh method, and the Hirota bilinear method [3][4][5][6][7][8][9][10][11][12][13][14][15][16] are mostly used in addition to other techniques. The Hirota's bilinear method is mostly used for the determination of multiple soliton solutions for a vast number of nonlinear equations.…”

Dynamics of interaction between solitary and rogue wave of the space-time fractional Broer–Kaup models arising in shallow water of harbor and coastal zone

“…Such hip in natural structures, solitons can similarly be formed in laboratories as dual plasma schemes [13,14], Joseph-son junctions [15,16] and so on. With this point of view, deriving soliton and its interaction solution of nonlinear wave models attract a much interest of young scientist [17][18][19]. Currently, many scientists are working with considerable efforts on the fractional differential models as it gives the real properties of natural phenomena [20,21].…”