Related papers: On continual classes of evolution equations
Differential equations are derived which show how generalized Euler vector representations of the Euler rotation axis and angle for a rigid body evolve in time; the Euler vector is also known as a rotation vector or axis-angle vector. The…
This paper is part of a research project on relations between differential-difference matrix Lax representations (MLRs) with the action of gauge transformations and discrete Miura-type transformations (MTs) for (nonlinear) integrable…
A recently proposed discrete version of the Schrodinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated to this spectral problem is derived. It is shown that a discrete…
An evolution-type differential equation encodes the intersection theory of tautological classes on the Hilbert scheme of a family of nodal curves.
We deal with the existence of solutions having L2 regularity for a class of non autonomous evolution equations. Associated with the equation, a general non local condition is studied. The technique we used combines a finite dimensional…
Evolution of structure functions and their moments at low and moderate $Q^2$ is studied in the chiral field theory. Evolution equations based on perturbation expansion in the coupling constant of the effective theory are derived and solved…
Lamb has identified a certain class of moving space curves with soliton equations. We show that there are two other classes of curve evolution that may be so identified. Hence three distinct classes of curve evolution are associated with a…
Obstacles to integrability in perturbed evolution equations are overcome by allowing higher-order terms in the expansion of the solution to depend explicitly on time and position. With a special expansion algorithm, obstacles vanish…
We investigate the initial-value problem of the non-linear Liouville hierarchy. For the general form of the interaction potential we construct an explicit solution in terms of an expansion over particle clusters whose evolution is described…
We consider three classical models of biological evolution: (i) the Moran process, an example of a reducible Markov Chain; (ii) the Kimura Equation, a particular case of a degenerated Fokker-Planck Diffusion; (iii) the Replicator Equation,…
In this work we study the space of derivations of non-degenerate evolution algebras. We improve some results obtained recently in the literature and, as a consequence, we advance in the description of the derivations for $n$-dimensional…
We study normal forms of scalar integrable dispersive (non necessarily Hamiltonian) conservation laws via the Dubrovin-Zhang perturbative scheme. Our computations support the conjecture that such normal forms are parametrised by infinitely…
We derive a new exact evolution equation for the scale dependence of an effective action. The corresponding equation for the effective potential permits a useful truncation. This allows one to deal with the infrared problems of theories…
An alternative approach - nonequilibrium evolution thermodynamics, is compared with classical Landau approach. A statistical justification of the approach is carried out with help of probability distribution function on an example of a…
A large class of initial-boundary value problems of linear evolution partial differential equations formulated on the half-line is analyzed via the unified transform method. In particular, explicit formulae are presented for the generalized…
A general formulation of zero curvature connections in a principle bundle is presented and some applications are discussed. It is proved that a related connection based on a prolongation in an associated bundle remains zero curvature as…
We suggest the method for group classification of evolution equations admitting nonlocal symmetries which are associated with a given evolution equation possessing nontrivial Lie symmetry. We apply this method to second-order evolution…
Using the fact that Miura transformation can be expressed in the form of gauge transformation connecting the KdV and mKdV equations, we discuss the derivation of the B\"acklund transformation and its Miura-gauge transformation connecting…
We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the…
Moments are expectation values of products of powers of position and momentum, taken over quantum states (or averages over a set of classical particles). For free particles, the evolution in the quantum case is closely related to that of a…