Results 21 to 30 of about 863 (58)

Darboux transformation for classical acoustic spectral problem

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 49, Page 3123-3142, 2003., 2003
We study discrete isospectral symmetries for the classical acoustic spectral problem in spatial dimensions one and two by developing a Darboux (Moutard) transformation formalism for this problem. The procedure follows steps similar to those for the Schrödinger operator. However, there is no one‐to‐one correspondence between the two problems.
A. A. Yurova, A. V. Yurov, M. Rudnev
wiley   +1 more source

Prolongation structure of the Krichever-Novikov equation [PDF]

, 2002
We completely describe Wahlquist-Estabrook prolongation structures (coverings) dependent on u, u_x, u_{xx}, u_{xxx} for the Krichever-Novikov equation u_t=u_{xxx}-3u_{xx}^2/(2u_x)+p(u)/u_x+au_x in the case when the polynomial p(u)=4u^3-g_2u-g_3 has ...
Igonin, Sergei, Martini, Ruud
core   +5 more sources

The equivalence between the Hamiltonian and Lagrangian formulations for the parametrization‐invariant theories

International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 1, Page 9-14, 2002., 2002
The link between the treatment of singular Lagrangians as field systems and the canonical Hamiltonian approach is studied. It is shown that the singular Lagrangians as field systems are always in exact agreement with the canonical approach for the parametrization invariant theories.
S. I. Muslih
wiley   +1 more source

About seismic tomography algorithm in the prediction of geological dislocations in coal seams

Горные науки и технологии, 2018
An algorithm for processing of crosshole seismic survey data enabling recognizing the type and evaluate the characteristics of geological anomalies using a system of criteria is described.
A. V. Antsiferov, A. A. Glukhov, V. V. Tumanov, D. V. Son, S. P. Olenjuk   +4 more
doaj   +1 more source

On the compatible weakly nonlocal Poisson brackets of hydrodynamic type

International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 10, Page 587-614, 2002., 2002
We consider the pairs of general weakly nonlocal Poisson brackets of hydrodynamic type (Ferapontov brackets) and the corresponding integrable hierarchies. We show that, under the requirement of the nondegeneracy of the corresponding “first” pseudo‐Riemannian metric g(0) νμ and also some nondegeneracy requirement for the nonlocal part, it is possible to
Andrei Ya. Maltsev
wiley   +1 more source

Compatible flat metrics

Journal of Applied Mathematics, Volume 2, Issue 7, Page 337-370, 2002., 2002
We solve the problem of description of nonsingular pairs of compatible flat metrics for the general N‐component case. The integrable nonlinear partial differential equations describing all nonsingular pairs of compatible flat metrics (or, in other words, nonsingular flat pencils of metrics) are found and integrated.
Oleg I. Mokhov
wiley   +1 more source

High order multiscale analysis of discrete integrable equations [PDF]

Open Communications in Nonlinear Mathematical Physics
In this article we present the results obtained applying the multiple scale expansion up to the order $\varepsilon^6$ to a dispersive multilinear class of equations on a square lattice depending on 13 parameters. We show that the integrability conditions
Rafael Hernandez Heredero, Decio Levi, Christian Scimiterna   +2 more
doaj   +1 more source

Non-commutative rational Yang-Baxter maps [PDF]

, 2013
Starting from multidimensional consistency of non-commutative lattice modified Gel'fand-Dikii systems we present the corresponding solutions of the functional (set-theoretic) Yang-Baxter equation, which are non-commutative versions of the maps arising ...
Doliwa, Adam
core   +2 more sources

Chains of KP, semi‐infinite 1‐Toda lattice hierarchy and Kontsevich integral

Journal of Applied Mathematics, Volume 1, Issue 4, Page 175-193, 2001., 2001
There are well‐known constructions of integrable systems that are chains of infinitely many copies of the equations of the KP hierarchy “glued” together with some additional variables, for example, the modified KP hierarchy. Another interpretation of the latter, in terms of infinite matrices, is called the 1‐Toda lattice hierarchy.
L. A. Dickey
wiley   +1 more source

Gardner's deformations of the Boussinesq equations

, 2006
Using the algebraic method of Gardner's deformations for completely integrable systems, we construct the recurrence relations for densities of the Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending the Magri schemes for these
Karasu, Atalay, Kiselev, Arthemy V.
core   +1 more source