Linearizability and Nonlocal Superposition for Nonlinear Transport Equation with Memory

New Nonlocal Symmetries of Diffusion-Convection Equations and Their Connection with Generalized Hodograph Transformation

“…Here b(v, t) is an arbitrary solution of the linear heat Equation (21). An application of the nonlocal transformation Equation (25) to Equation (4) generates an expression which after simplification vanishes identically on the manifold defined by Equation (7) and expression v x + b/2b v = 0 with its differential consequences.…”

“…The characteristic Equation (27) determines nonlocal transformation with additional variables, which connects Equations (4) and (7) taking into account Equation (21) and condition Equation (20). Additional independent variable v(x, t) is determined by Equation (7) and additional dependent variable b(v, t) is an arbitrary solution of the Equation (21).…”

“…To deduce the characteristic equation, which corresponds to Equation (29) and determines nonlocal symmetry of the Equation (4) in terms of variables x, t, u(x, t), we need to exclude a variable v(x, t) from expression Equation (30), where b (v, t) is a function belonging to the set of solutions of the linear heat Equation (21). New designations will be necessary for us in what follows.…”

“…This approach is based on the nonlocal transformations technic [16][17][18][19][20][21], which we regularly use for study of symmetries of the given nonlinear equations in [1] and in the current paper.…”