Related papers: On integrable conservation laws
Structure-preserving algorithms for solving conservative PDEs with added linear dissipation are generalized to systems with time-dependent damping/driving terms. This study is motivated by several PDE models of physical phenomena, such as…
It was shown recently that Frobenius reduction of the matrix fields reveals interesting relations among the nonlinear Partial Differential Equations (PDEs) integrable by the Inverse Spectral Transform Method ($S$-integrable PDEs),…
Structure-preserving particle methods have recently been proposed for a class of nonlinear continuity equations, including aggregation-diffusion equation in [J. Carrillo, K. Craig, F. Patacchini, Calc. Var., 58 (2019), pp. 53] and the…
We consider time-harmonic electromagnetic wave equations in composites of a dispersive material surrounded by a classical material. In certain frequency ranges this leads to sign-changing permittivity and/or permeability. Previously meshing…
Typical fully conservative discretizations of the Euler compressible single or multi-component fluid equations governed by a real-fluid equation of state exhibit spurious pressure oscillations due to the nonlinearity of the thermodynamic…
We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively…
Hadronization models based on local string-breaking dynamics are typically Markovian by construction, yet the physical ensemble of final states is shaped by global constraints that couple the entire fragmentation trajectory. Recasting…
In this paper we study generalized classes of volume preserving multidimensional integrable systems via Nambu--Poisson mechanics. These integrable systems belong to the same class of dispersionless KP type equation. Hence they bear a close…
We continue the investigation of the correspondence between systems of conservation laws and congruences of lines in projective space. Relationship between "additional" conservation laws and hypersurfaces conjugate to a congruence is…
We fill the two main remaining gaps in the full classification of non-degenerate planar traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under smooth perturbations. On one hand we…
Under a precise genuine nonlinearity assumption we establish the decay of entropy solutions of a multidimensional scalar conservation law with merely continuous flux.
We consider partial differential equations (PDE) of drift-diffusion type in the unit interval, supplemented by either two conservation laws or by a conservation law and a further boundary condition. We treat two different cases: (i) uniform…
A general procedure for constructing conservative numerical integrators for time dependent partial differential equations is presented. In particular, linearly implicit methods preserving a time discretised version of the invariant is…
In this paper we consider affine Toda systems defined on the half-plane and study the issue of integrability, i.e. the construction of higher-spin conserved currents in the presence of a boundary perturbation. First at the classical level…
In this paper, we study explicit correspondences between the integrable Novikov and Sawada-Kotera hierarchies, and between the Degasperis-Procesi and Kaup-Kupershmidt hierarchies. We show how a pair of Liouville transformations between the…
The Dubrovin-Zhang hierarchy is a Hamiltonian infinite-dimensional integrable system associated to a semi-simple cohomological field theory or, alternatively, to a semi-simple Dubrovin-Frobenius manifold. Under an extra assumption of…
Let E be an unbounded open (or closed) domain in Euclidean space of dimension greater or equal to two. We present conservativeness criteria for (possibly reflected) diffusions with state space E that are associated to fairly general…
In this note a new way to construct the characteristics of conservations laws of integrable chiral-type systems is proposed.
All the Doubly Special Relativity (DSR) models studied in literature so far involve a deformation of the energy conservation rule that forces us to release the hypothesis of the additivity of the energy for composite systems. In view of the…
The aim article is to contribute to the definition of a versatile language for metastability in the context of partial differential equations of evolutive type. A general framework suited for parabolic equations in one dimensional bounded…