From time to time one finds claims in the literature that first integrals/invariants
of Lagrangian systems are nonnoetherian. Such claims diminish the contribution of
Noether in the topic of integrability. We provide an explicit demonstration of noethe-
rian symmetries associated with the integrals...
We apply singularity analysis to a caricature of the simplified multistrain model of
Castillo-Chavez and Feng (J Math Biol 35 (1997) 629–656) for the transmission of
tuberculosis and the coupled two-stream vector-based model of Feng and Velasco-
Hern ?andez (J Math Biol 35 (1997) 523–544) to identify...
Using the complete group classification of semilinear differential equations on the
three-dimensional Heisenberg group H, carried out in a preceding work, we estab-
lish the conservation laws for the critical Kohn-Laplace equations via the Noether’s
We introduce a (2+1)-dimensional extension of the 1-dimensional Toda lattice hierar-
chy. The hierarchy is given by two different formulations. For the first formulation,
we obtain the bilinear identity for the ? -functions and construct explicit solutions ex-
pressed by Wronski determinants. For...
A necessary condition for the existence of conserved densities and fluxes of a
differential-difference equation which depend on q shifts, for q sufficiently large, is presented. This condition depends on the eigenvalues of the leading terms in the differential-difference equation. It also gives, explicitly,...
The superposition formulas for solutions of integrable vector evolutionary equations on
a sphere are constructed by means of auto-B ?acklund transformation. The equations
under consideration were obtained earlier by Sokolov and Meshkov in the frame of the
Anisotropic phenomena can be observed almost everywhere in nature. This makes
them important sub jects for theoretical and experimental studies. In this work, we
focus on the study of anisotropic quasi-self-similar signals. It holds that the classical
multifractal formalism in all its formulations...