相关论文: Intrinsic Formulation of Geometric Integrability a…

We construct an infinite hierarchy of nonlocal conservation laws for the $ABC$ equation $A u_t\,u_{xy}+B u_x\,u_{ty}+C u_y\,u_{tx} = 0$, where $A,B,C$ are constants and $A+B+C\neq 0$, using a nonisospectral Lax pair. As a byproduct, we…

A systematic study of the discrete second order projective system is presented, complemented by the integrability analysis of the associated multilinear mapping. Moreover, we show how we can obtain third order integrable equations as the…

We present a detailed analysis of the structure of the conservation laws in quantum integrable chains of the XYZ-type and in the Hubbard model. With the use of the boost operator, we establish the general form of the XYZ conserved charges…

The system of equations of one-dimensional shallow water over uneven bottom in Euler's and Lagrange's variables is considered. Intermediate system of equations is introduced. Hydrodynamic conservation laws of intermediate system of…

We introduce a sound and complete coinductive proof system for reachability properties in transition systems generated by logically constrained term rewriting rules over an order-sorted signature modulo builtins. A key feature of the…

Every simplest potential conservation law of any (1+1)-dimensional linear evolution equation of even order proves induced by a local conservation law of the same equation. This claim is true also for linear simplest potential conservation…

We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are generated by any symmetry of the operator, including…

Lagrangian multiforms provide a variational framework for describing integrable hierarchies. This thesis presents two approaches for systematically constructing Lagrangian one-forms, which cover the case of finite-dimensional integrable…

A two-parameters family of Backlund transformations for the classical elliptic Gaudin model is constructed. The maps are explicit, symplectic, preserve the same integrals as for the continuous flows and are a time discretization of each of…

In this paper we will present Lagrangian and Hamiltonian $k$-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using…

One dimensional systems sometimes show pathologically slow decay of currents. This robustness can be traced to the fact that an integrable model is nearby in parameter space. In integrable models some part of the current can be conserved,…

This article explores the exceptional integrability property of a family of higher-order Benjamin-Bona-Mahony (BBM)-type nonlinear dispersive equations. Here, we highlight its deep relationship with a generalized infinite hierarchy of the…

We give a complete description of nontrivial local conservation laws of all orders for a natural generalization of the nonlinear progressive wave equation and, in particular, show that there is an infinite number of such conservation laws.

A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial…

In this article we describe the applications of the relative entropy framework. In particular uniqueness of an entropy solution is proven for a scalar conservation law, using the notion of measure-valued entropy solutions. Further we survey…

Recently, a hydrodynamic description of local equilibrium dynamics in quantum integrable systems was discovered. In the diffusionless limit, this is equivalent to a certain "Bethe-Boltzmann" kinetic equation, which has the form of an…

We study a scalar integro-differential conservation law. The equation was first derived in [2] as the slow erosion limit of granular flow. Considering a set of more general erosion functions, we study the initial boundary value problem for…

In this work, following the paper by Romain Ruzziconi and C\'eline Zwikel \cite{Ruzziconi:2020wrb} we extend the questions of conservation, integrability and renormalization in Bondi gauge and in GR to the theory of Topological Massive…

Derivation of governing equations for multiphase flow on the base of thermodynamically compatible systems theory is presented. The mixture is considered as a continuum in which the multiphase character of the flow is taken into account. The…

The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems…