Related papers: Topological charges and conservation laws involvin…
In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is obtained by using both continuous and discontinuous…
The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the previous notions of self-adjoint and quasi self-adjoint…
Topological edge states in systems of two (or more) dimensions offer scattering-free transport, exhibiting robustness to inhomogeneities and disorder. In a different domain, time-modulated systems, such as photonic time crystals (PTCs),…
The set of real finite-gap Sine-Gordon solutions corresponding to a fixed spectral curve consists of several connected components. A simple explicit description of these components obtained by the authors recently is used to study the…
We develop a pathwise theory for scalar conservation laws with quasilinear multiplicative rough path dependence, a special case being stochastic conservation laws with quasilinear stochastic dependence. We introduce the notion of pathwise…
The problem of topology change description in gravitation theory is analized in detailes. It is pointed out that in standard four-dimensional theories the topology of space may be considered as a particular case of boundary conditions (or…
The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation…
Active matter encompasses different nonequilibrium systems in which individual constituents convert energy into non-conservative forces or motion at the microscale. This review provides an elementary introduction to the role of topology in…
Conservation laws of a class of time-dependent damped nonlinear multidimensional wave equations are derived by Noether's theorem. For arbitrary nonzero damping coefficient and nonlinear interaction term, its infinitesimal variational…
We succeed in writing 2-dimensional conformally invariant non-linear elliptic PDE (harmonic map equation, prescribed mean curvature equations...etc) in divergence form. This divergence free quantities generalize to target manifolds without…
In this technical note, we consider a dynamic linear, cantilevered rectangular plate. The evolutionary PDE model is given by the fourth order plate dynamics (via the spatial biharmonic operator) with clamped-free-free-free boundary…
We establish local-in-time existence and uniqueness results for nonlocal conservation laws with a nonlinear mobility, in several space dimensions, under weak assumptions on the kernel, which is assumed to be bounded and of finite total…
Preservation of linear and quadratic invariants by numerical integrators has been well studied. However, many systems have linear or quadratic observables that are not invariant, but which satisfy evolution equations expressing important…
This paper extends, to a class of systems of semi-linear hyperbolic second order PDEs in three variables, the geometric study of a single nonlinear hyperbolic PDE in the plane as presented in [Anderson I.M., Kamran N., Duke Math. J. 87…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…
Nonlocally related partial differential equation (PDE) systems are useful in the analysis of a given PDE system. It is known that each local conservation law of a given PDE system systematically yields a nonlocally related system. In this…
Epsilon-near-zero and epsilon near-pole materials enable reflective systems supporting a class of symmetry-protected and accidental embedded eigenstates (EE) characterized by a diverging phase-resonance. Here we show that pairs of…
We study the conservation laws associated with the asymptotic Poincare symmetry of spacetime in the general teleparallel theory of gravity. Demanding that the canonical Poincare generators have well defined functional derivatives in a…
A direct method for the computation of polynomial conservation laws of polynomial systems of nonlinear partial differential equations (PDEs) in multi-dimensions is presented. The method avoids advanced differential-geometric tools. Instead,…
In this work we study the general system of geodesic equations for the case of a massive particle moving on an arbitrary curved manifold. The investigation is carried out from the symmetry perspective. By exploiting the parametrization…