相关论文: On Symmetries and Conservation Laws of the Majda-B…

In the present paper the non-Noether symmetries of the Toda model, nonlinear Schodinger equation and Korteweg-de Vries equations (KdV and mKdV) are discussed. It appears that these symmetries yield the complete sets of conservation laws in…

Lie symmetry analysis has been applied to the extended Boiti-Leon-Manna-Pempinelli (eBLMP) equation. This system illustrates the exchange of information between two waves with distinct dispersion characteristics. The optimal system of the…

The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…

We provide a complete classification of generalized and formal symmetries and local conservation laws for an evolution equation which generalizes the Kawahara equation having important applications in the study of plasma waves and…

A systematic method to derive the Hamiltonian and Nambu form for the shallow water equations, using the conservation for energy and potential enstrophy, is presented. Different mechanisms, such as vortical flows and emission of gravity…

Triple systems with low hierarchical structure are common throughout the Universe, including examples such as high-altitude lunar satellites influenced by the Earth, planetary satellites perturbed by the Sun, and stellar binaries affected…

The paper takles a procedure which allow to extend some linear, wave type equations to the study of nonlinear models. More concretely, we present a practical way to generate the largest class of a given form of second order differential…

For the hyperbolic system of quasilinear first-order partial differential equations, linearizable by hodograph transformation, the conservation laws are used to solve the Cauchy problem. The equivalence of the initial problem for…

In recent work we constructed completely general conservation laws for energy and linear and angular momentum of extended systems in general relativity based on the notion of a rigid quasilocal frame (RQF). We argued at a fundamental level…

Furthering the development of Da Lio-Gianocca-Rivi\`ere's Morse stability theory (arXiv:2212.03124) that was first applied to harmonic maps between manifolds and later extended to the case of Willmore immersions (arXiv:2306.04608-04609), we…

A conservation law theorem stated by N. Ibragimov along with its subsequent extensions are shown to be a special case of a standard formula that uses a pair consisting of a symmetry and an adjoint-symmetry to produce a conservation law…

In this paper we introduce a new property of two-dimensional integrable systems -- existence of infinitely many local three-dimensional conservation laws for pairs of integrable two-dimensional commuting flows. Infinitely many…

A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that…

We study the linearised Einstein--Maxwell equations on the Reissner--Nordstr\"om spacetime and derive the canonical energy conservation law in double null gauge. In the spirit of the work of Holzegel and the second author, we avoid any use…

We study Hamiltonian difference schemes for scalar conservation laws with monotone flux function and establish the existence of a three-parameter family of periodic travelling waves (wavetrains). The proof is based on an integral equation…

In this paper we consider a new class of Hamiltonian hydrodynamic type systems, whose conservation laws are polynomial with respect to one of field variables.

This article provides an overview on various conservation laws for polyharmonic maps between Riemannian manifolds. Besides recalling that the variation of the energy for polyharmonic maps with respect to the domain metric gives rise to the…

We analyze a system of three two-dimensional nonlinear Schr\"odinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time…

The reduced-complexity models developed by Edward Lorenz are widely used in atmospheric and climate sciences to study nonlinear aspect of dynamics and to demonstrate new methods for numerical weather prediction. A set of inviscid Lorenz…

We prove that $p $-harmonic systems with antisymmetric potentials can be written in divergence form as a conservation law. This extends to the $p$-harmonic framework the original work from 2006 of the second author for $p=2$…