Integrable Hamiltonian equations of fifth order with the Hamiltonian operator $\boldsymbol D_x$
All non-equivalent integrable evolution equations of the fifth order of the form $u_t=D_x\frac{δH}{δu}$ are found.
math-ph↗
arXiv subjects
A. G. Meshkov
Publications and source records attributed to A. G. Meshkov.
Integrable evolution Hamiltonian equations of the third order with the Hamiltonian operator $\boldsymbol D_x$
All non-equivalent integrable evolution equations of third order of the form $u_t=D_x\frac{δH}{δu}$ are found.
math-ph↗
Integrable evolution equations with constant separant
The survey provides classification results for integrable one-field evolution equations of orders 2, 3 and 5 with the constant separant. The classification is based on necessary integrability conditions following from the existence of the formal recursion operator for integrable equations. Recurrent formulas for the whole infinite sequence of necessary conditions are presented for the first time. The most of the classification statements can be found in papers by S.I. Svinilupov and V.V. Sokolov but the proofs have never been published before. The result concerning the fifth order equations is stronger than obtained before.
nlin.SI↗
Integrable hyperbolic equations of sin-Gordon type
A complete list of nonlinear one-field hyperbolic equations having generalized integrable x- and y-symmetries of the third order is presented. The list includes both sin-Gordon type equations and equations linearizable by differential substitutions.
nlin.SI↗
Nonlocal symmetries of integrable two-field divergent evolutionary systems
Nonlocal symmetries for exactly integrable two-field evolutionary systems of the third order have been computed. Differentiation of the nonlocal symmetries with respect to spatial variable gives a few nonevolutionary systems for each evolutionary system. Zero curvature representations for some new nonevolution systems are presented.
nlin.SI↗
New integrable string-like fields in 1+1 dimensions
The symmetry classification method is applied to the string-like scalar fields in two-dimensional space-time. When the configurational space is three-dimensional and reducible we present the complete list of the systems admiting higher polynomial symmetries of the 3rd, 4th and 5th-order.
solv-int↗