On construction of recursion operators from Lax representation

Gurses, M
Karasu, Atalay
Sokolov, VV
In this work we develop a general procedure for constructing the recursion operators for nonlinear integrable equations admitting Lax representation. Several new examples are given. In particular, we find the recursion operators for some KdV-type systems of integrable equations. (C) 1999 American Institute of Physics. [S0022-2488(99)03212-0].


Recursion operators of some equations of hydrodynamic type
GÜRSES, METİN; Zheltukhın, Kostyantyn (2001-03-01)
We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N=2 and N=3 containing the equations of shallow water waves and its generalizations with their first two general symmetries and their recursion operators. We also discuss a reduction of N+1 systems to N systems of some new equations of hydrodynamic type. (C) 2001 American Institute of Physics.
On the consistency of the solutions of the space fractional Schroumldinger equation (vol 53, 042105, 2012)
Bayin, Selcuk S. (2012-08-01)
Recently we have reanalyzed the consistency of the solutions of the space fractional Schroumldinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are consistent. In this comment, for clarity, we present additional information about the critical integrals and describe how their analytic continuation is accomplished.
On singular solutions of implicit second-order ordinary differential equations
Bhupal, Mohan Lal (2003-01-01)
In this note we discuss the notion of singular solutions of completely integrable implicit second-0rder ordinary differential equations. After restricting the class of admissible equations we give conditions under which singular solutions occur in 1-parameter families and as isolated objects. © 2003 by the University of Notre Dame. All rights reserved.
On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems
AKBAŞ, MERAL; Kaya, Serap; Kaya Merdan, Songül (2017-07-01)
We prove long-time stability of linearly extrapolated BDF2 (BDF2LE) timestepping methods, together with finite element spatial discretizations, for incompressible Navier-Stokes equations (NSE) and related multiphysics problems. For the NSE, Boussinesq, and magnetohydrodynamics schemes, we prove unconditional long time L-2 stability, provided external forces (and sources) are uniformly bounded in time. We also provide numerical experiments to compare stability of BDF2LE to linearly extrapolated Crank-Nicolso...
On the discretization of Laine equations
Zheltukhın, Kostyantyn (2018-01-01)
We consider the discretization of Darboux integrable equations. For each of the integrals of a Laine equation we constructed either a semi-discrete equation which has that integral as an n-integral, or we proved that such an equation does not exist. It is also shown that all constructed semi-discrete equations are Darboux integrable.
Citation Formats
M. Gurses, A. Karasu, and V. Sokolov, “On construction of recursion operators from Lax representation,” JOURNAL OF MATHEMATICAL PHYSICS, pp. 6473–6490, 1999, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35370.