Lie symmetry analysis, symmetry reductions with exact solutions, and conservation laws of (2+1)‐dimensional Bogoyavlenskii‐Schieff equation of higher order in plasma physics

Abstract

In this article, similarity reductions of the (2+1)-dimensional Bogoyavlenskii-Schieff equation of higher order have been done by Lie group method. We have determine the geometric vector field, infinitesimal generators, symmetric groups, and commutator table of Lie algebra with the help of Lie symmetry analysis. The new close form solutions and similarity solutions of the (2+1)-dimensional Bogoyavlenskii-Schieff equation of higher order have been determined from the reduction equations. Also, the conservation laws have been derived by invoking the new conservation theorem proposed by Ibragimov. KEYWORDS (2 + 1)-dimensional Bogoyavlenskii-Schieff equation, conservation laws, infinitesimal generator, Lie symmetry analysis, symmetry reductions MSC CLASSIFICATION 70H33; 35L65; 35G20 Math Meth Appl

Lie symmetries, solitary wave solutions, and conservation laws of coupled KdV‐mKdV equation for internal gravity waves

“…This section introduces conservation laws for KdV-mKdV equation associated with Lie symmetry analysis [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. The adjoint equation and Lagrangian operator are determined using Noether's theorem.…”

“…Therefore, nonlinear partial differential equations (NPDEs) play a major role in modeling of these natural waves and several wave phenomena as well. The massive applications of NPDEs can be seen in various fields of mathematical sciences, biological sciences, nonlinear optics, electromagnetic theory, quantum theory, optical fiber, plasma physics, heat transfer, fluid dynamics, and so forth [1‐32,33,34]. The NPDEs are difficult to handle with traditional methods, so a large number of methods such as Darboux transformations [1], Fan's subequation method [3], extended mapping method [4], sub‐ODE method [5], extended tanh method [6], amplitude ansatz method [7], WTC truncation method [8], nonlocal symmetry method [9], and similarity transformation method [10–34] are evolved to derive exact solutions.…”

“…KdV‐mKdV equation is widely applied in several contexts as density stratified ocean, impact of external forces, internal gravity waves, dust‐ion acoustic waves, traffic flow problems, and so forth [1–10]. To accomplish the exact solution of governing equation, authors are motivated from previous researches to employ similarity transformation method via Lie group theory and derive conserved quantities [1‐32,33,34]. The method depends on invariance property under one parameter transformation.…”

Lie symmetries and exact solutions for a fourth‐order nonlinear diffusion equation

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

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