Nonlinear dynamics of (2 + 1)‐dimensional Bogoyavlenskii–Schieff equation arising in plasma physics

Abstract

In this literature, the dynamic characteristics of the Bogoyavlenskii–Schieff equation in (2 + 1)‐dimension that arises in plasma physics are studied. Several characteristics of multi‐soliton solutions, complex rogue wave, M‐lump solutions, fusion solutions, and interaction phenomena between M‐lump and soliton solutions also with a fusion solution are discussed. A logarithmic variable transform is used to convert the studied nonlinear equation to a Hirota trilinear form. For all solutions, three‐dimensional figures are presented to more understand its dynamic behaviors. All findings are recent, and no experts have reported them.

Multi-solutions with specific geometrical wave structures to a nonlinear evolution equation in the presence of the linear superposition principle

“…It should be emphasized, however, that numerous approaches such as the Lie symmetric analysis and its application [9][10][11][12][13][14], the Kudryashov method [15,16], the tanhcoth method [17], the improved Sardar-subequation [18], the new generalized auxiliary equation method [19], and other techniques [20][21][22][23][24] have been employed for generating interaction phenomena for nonlinear differential equations. Values are assigned to these constant coefficients in particular conditions to ensure that solutions exist [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Nonetheless, it is worth emphasizing that the problem of dealing with such interactions has yet to be studied.…”

Extended Calogero-Bogoyavlenskii-Schiff equation and its dynamical behaviors

“…Furthermore, Manakov et al discovered in [9] that the interactions of lump waves do not result in a pattern of phase changes. Regarding that, many powerful methods for finding the lump solutions of NPDEs have been developed over the past decades, including the long-wave limit approach [7,10], the nonlinear superposition formulae [11], the inverse scattering transformation [12,13], the invariance and Lie symmetry analysis [14,15], the Bäklund transformation [16,17], the bilinear neural network method [18][19][20][21][22][23][24], the Darboux transformation [25,26] and the Hirota bilinear method [27][28][29][30][31], Symbolic computation method [32][33][34][35] and other different methods [36][37][38][39][40][41][42][43]. Among the approaches stated above, taking a 'long wave' limit of the corresponding N-soliton solutions plays an important role in the investigation of M-lump solutions for nonlinear partial differential equations.…”