相关论文: On symmetries and conservation laws of a Gardner e…
The method of separation of variables is significant, it has been applied to physics, engineering , chemistry and other fields. It allows to reduce the diffculity of problems by separating the variables from partial differential equation…
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 strict self-adjointness and quasi self-adjointness introduced…
Backgrounds are pervasive in almost every application of general relativity. Here we consider the Lagrangian formulation of general relativity for large perturbations with respect to a curved background spacetime. We show that Noether's…
The nonlinear partial differential equations describing the spin dynamics of Heisenberg ferro and antiferromagnet are studied by Lie transformation group method. The generators of the admitted variational Lie symmetry groups are derived and…
We study the Gibbons-Tsarev equation $z_{yy} + z_x z_{xy} - z_y z_{xx} + 1 = 0$ and, using the known Lax pair, we construct infinite series of conservation laws and the algebra of nonlocal symmetries in the covering associated with these…
We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives. For…
We study conservation laws and potential symmetries of (systems of) differential equations applying equivalence relations generated by point transformations between the equations. A Fokker-Planck equation and the Burgers equation are…
The paper is devoted to the group analysis of equations of motion of two-dimensional uniformly stratified rotating fluids used as a basic model in geophysical fluid dynamics. It is shown that the nonlinear equations in question have a…
In this paper, we introduce a Lagrange multiplier approach to construct linearly implicit energy-preserving schemes of arbitrary order for general Hamiltonian PDEs. Unlike the widely used auxiliary variable methods, this novel approach does…
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the…
Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…
Given a class of differential equations with arbitrary element, the problems of symmetry group, nonclassical symmetry and conservation law classifications are to determine for each member the structure of its Lie symmetry group, conditional…
The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be…
Quasi-Noether differential systems are more general than variational systems and are quite common in mathematical physics. They include practically all differential systems of interest, at least those that have conservation laws. In this…
The conservation laws of electromagnetism, and implicitly all theories built from quadratic Lagrangians, are extended to a continuum of nonlocal versions. These are associated with symmetries of a class of equal time field correlation…
It's well known that Noether symmetries lead to the conservation laws. Conserved quantities are constructed out of generator of the symmetry - invariant Hamiltonian vector field. Considering more general class of vector fields -…
The relations between two construction methods (called multiplier and embedding methods) for conserved currents of general systems of ordinary or partial differential equations (DEs) are investigated. Recent studies indicate that the…
In this work we study variational properties of approximate solutions of scalar conservation laws. Solutions of this type are described by a kinetic equation which is similar to the kinetic representation of admissible weak solutions due to…
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…
For systems of partial differential equations in three spatial dimensions, dynamical conservation laws holding on volumes, surfaces, and curves, as well as topological conservation laws holding on surfaces and curves, are studied in a…