Remarks on certain two-component systems with peakon solutions

Autor: Hay, Mike, Hone, Andrew N. W., Novikov, Vladimir S., Wang, Jing Ping

We consider a Lax pair found by Xia, Qiao and Zhou for a family of two-component analogues of the Camassa-Holm equation, including an arbitrary function $H$, and show that this apparent freedom can be removed via a combination of a reciprocal transfo

Externí odkaz: http://arxiv.org/abs/1805.03323

Symmetry structure of integrable non-evolutionary equations

Autor: Novikov, Vladimir S., Wang, Jing Ping

We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic representation,

Externí odkaz: http://arxiv.org/abs/nlin/0702045

Partially integrable nonlinear equations with one higher symmetry

Autor: Mikhailov, Alexander V., Novikov, Vladimir S., Wang, Jing Ping

Publikováno v: J. Phys A: Math.Gen., 38 (2005), L337 - L341

In this paper we present a family of second order in time nonlinear partial differential equations, which have only one higher symmetry. These equations are not integrable, but have a solution depending on one arbitrary function.

Externí odkaz: http://arxiv.org/abs/nlin/0601047

Integrable Systems in Four Dimensions Associated with Six-Folds in Gr(4, 6)

Autor: Doubrov, Boris, Ferapontov, Evgeny V, Kruglikov, Boris, Novikov, Vladimir S

Publikováno v: Doubrov B, Ferapontov EV, Kruglikov BS, Novikov VS. Integrable Systems in Four Dimensions Associated with Six-Folds in Gr(4, 6). International mathematics research notices. 2019;2019(21):6585-6613

Externí odkaz: https://hdl.handle.net/10037/17941

Second-order PDEs in four dimensions with half-flat conformal structure

Autor: Berjawi, S., Ferapontov, Eugene V., Kruglikov, Boris, Novikov, Vladimir S

Publikováno v: Berjawi, Ferapontov, Kruglikov, Novikov. Second-order PDEs in four dimensions with half-flat conformal structure. Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. 2020;476(2233)

Externí odkaz: https://hdl.handle.net/10037/30904