Under investigation in this paper is the Kudryashov–Sinelshchikov equation, which
describes influence of viscosity and heat transfer on propagation of the pressure waves. The …

For systems of partial differential equations in three spatial dimensions, dynamical
conservation laws holding on volumes, surfaces, and curves, as well as topological …

In this article, we construct exact solutions to a quasilinear system of hyperbolic partial
differential equations which governs the dynamics of a thin film of a perfectly soluble anti …

We carry out an extensive investigation of conservation laws and potential symmetries for
the class of linear (1+ 1)-dimensional second-order parabolic equations. The group …

A bstract Higher-form symmetries are associated with transformations that only act on
extended objects, not on point particles. Typically, higher-form symmetries live alongside …

Any partial differential equation (PDE) system can be effectively analyzed through
consideration of its tree of nonlocally related systems. If a given PDE system has n local …

An algorithmic framework is presented to find an extended tree of nonlocally related systems
for a given system of differential equations (DEs). Each system in an extended tree is …

We perform the classification of nonlocal symmetries and obtain some exact solutions to the
system of nonlinear partial differential equations (PDEs), which describe a one-dimensional …

We introduce notions of equivalence of conservation laws with respect to Lie symmetry
groups for fixed systems of differential equations and with respect to equivalence groups or …

Based on the truncated Painlevé method and the Möbius (conformal) invariant form, the
nonlocal symmetry for the Drinfel'd-Sokolov-Wilson equation is derived. To use symmetry …