Results 31 to 40 of about 14,181 (315)

On integrable conservation laws

, 2014
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 many arbitrary
Moro, Antonio, Arsie, Alessandro, Lorenzoni, Paolo   +2 more
core   +1 more source

Two-component generalizations of the Camassa-Holm equation [PDF]

, 2017
A classification of integrable two-component systems of non-evolutionary partial differential equations that are analogous to the Camassa-Holm equation is carried out via the perturbative symmetry approach.
Novikov, Vladimir S., V.S. Novikov (7160981), Wang, Jing Ping, Hone, Andrew N.W., Jing Ping Wang (7161005), Andrew N.W. Hone (7161002)   +5 more
core   +1 more source

Discrete traveling waves in a Toda’s relay chain

Partial Differential Equations in Applied Mathematics
A relay version of the Toda’s chain is considered. For a system of m+1 identical oscillators connected in a ring, the applicability of the method of constructing periodic solutions in the form of discrete traveling waves is investigated.
A.A. Kutuzova, M.M. Preobrazhenskaia, A.S. Tokmachev   +2 more
doaj   +1 more source

Twistor Actions for Integrable Systems

Journal of High Energy Physics, 2021
Many integrable systems can be reformulated as holomorphic vector bundles on twistor space. This is a powerful organizing principle in the theory of integrable systems.
Robert F. Penna
doaj   +1 more source

Integrable viscous conservation laws

, 2015
We propose an extension of the Dubrovin-Zhang perturbative approach to the study of normal forms for non-Hamiltonian integrable scalar conservation laws. The explicit computation of the first few corrections leads to the conjecture that such normal forms
Moro, Antonio, Arsie, Alessandro, Lorenzoni, Paolo   +2 more
core   +1 more source

Non-integrability of a fifth order equation with integrable two-body dynamics [PDF]

, 2003
We consider the fifth order partial differential equation (PDE) u4x,t?5uxxt+4ut+uu5x+2uxu4x?5uu3x?10uxuxx+12uux=0, which is a generalization of the integrable Camassa-Holm equation.
Holm, Darryl D., Hone, Andrew N.W.
core   +1 more source

Averaging method for problems on quasiclassical asymptotics

Современная математика: Фундаментальные направления
The averaging method is developed for operators with rapidly oscillating coefficients, intended for use in problems of quasiclassical asymptotics and not assuming a periodic structure of coefficient oscillations.
S. Yu. Dobrokhotov, V. E. Nazaikinskii
doaj   +1 more source

On Classification of Integrable Davey-Stewartson Type Equations

, 2013
This paper is devoted to the classification of integrable Davey-Stewartson type equations. A list of potentially deformable dispersionless systems is obtained through the requirement that such systems must be generated by a polynomial dispersionless Lax ...
Novikov, Vladimir, Huard, Benoit
core   +1 more source

Asymptotic approximation of fading mode in neurooscillator dynamics

Partial Differential Equations in Applied Mathematics
We consider a system consisting of two delay differential equations with a large parameter, modeling the association of a pair of neurooscillators. The unknown functions describe the changes in the normalized membrane potentials of neurons over time ...
M.M. Preobrazhenskaia, V.K. Zelenova
doaj   +1 more source

On matrix Lax representations and constructions of Miura-type transformations for differential–difference equations

Partial Differential Equations in Applied Mathematics
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 differential ...
Evgeny Chistov, Sergei Igonin
doaj   +1 more source