58 citations · 765 across the 50 of their papers we have counts for
6 papers · 1 filter
Symmetries and conservation laws for the Karczewska--Rozmej--Rutkowski--Infeld equation
A. Sergyeyev, R. F. Vitolo
We give a complete description of generalized symmetries and local conservation laws for the fifth-order Karczewska--Rozmej--Rutkowski--Infeld equation describing shallow water wav…
Conservation laws and normal forms of evolution equations
Roman O. Popovych, Artur Sergyeyev
We study local conservation laws for evolution equations in two independent variables. In particular, we present normal forms for the equations admitting one or two low-order conse…
Reciprocal transformations and deformations of integrable hierarchies
A. Sergyeyev
We present changes of variables that transform new integrable hierarchies found by Szablikowski and Błaszak using the -matrix deformation technique [J. Math. Phys. 47 (2006), pa…
Infinite hierarchies of nonlocal symmetries of the Chen--Kontsevich--Schwarz type for the oriented associativity equations
Artur Sergyeyev
We construct infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using solutions of associated vector and scalar spectral problems. The symm…
Infinitely many local higher symmetries without recursion operator or master symmetry: integrability of the Foursov--Burgers system revisited
Artur Sergyeyev
We consider the Burgers-type system studied by Foursov, w_t &=& w_{xx} + 8 w w_x + (2-4α)z z_x, z_t &=& (1-2α)z_{xx} - 4αz w_x + (4-8α)w z_x - (4+8α)w^2 z + (-2+4α)z^3, (*) for whi…
Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility
Artur Sergyeyev
We show that under certain technical assumptions any weakly nonlocal Hamiltonian structure compatible with a given nondegenerate weakly nonlocal symplectic structure can be wri…