Nonlinear Self-Adjoint Classification of a Burgers-KdV Family of Equations

Abstract

The concepts of strictly, quasi, weak, and nonlinearly self-adjoint differential equations are revisited. A nonlinear self-adjoint classification of a class of equations with second and third order is carried out.

Symmetries and conservation laws of a time dependent nonlinear reaction-convection-diffusion equation

“…The result is given by the following statement. For detail of the self-adjoint classification of a class of equations with second and third order, one can see [19] and references therein. Proof.…”

“…are the total differentiations. Ibragimov [8] proved that (20) inherits all symmetries of (19). By using Noether's identity, one can obtain the formula of conservation law corresponding to every symmetry of (19).…”

“…By using Noether's identity, one can obtain the formula of conservation law corresponding to every symmetry of (19). (19) and (20). The conserved vector is given by…”

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

“…In addition, the concept of conservation laws is essential and widely used in the study of basic properties of the analytical solutions of NPDEs. In the field of physics, conservation laws give the conclusion of a physical system, and there are several conservation laws like conservation of mass and energy, conservation of natural resources, and conservation of rotational; those were discovered and expanded gradually over time.…”