58 citations · 765 across the 50 of their papers we have counts for
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Infinitely many conservation laws for generalized nonlinear progressive wave equation
A. Sergyeyev
We give a complete description of nontrivial local conservation laws of all orders for a natural generalization of the nonlinear progressive wave equation and, in particular, show…
Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model
Stanislav Opanasenko, Alexander Bihlo, Roman O. Popovych +1
We study the hydrodynamic-type system of differential equations modeling isothermal no-slip drift flux. Using the facts that the system is partially coupled and its subsystem reduc…
Integrable (3+1)-dimensional systems with rational Lax pairs
A. Sergyeyev
The search for new integrable (3+1)-dimensional partial differential systems is among the most important challenges in the modern integrability theory. It turns out that such a sys…
Recursion Operators for Multidimensional Integrable PDEs
A. Sergyeyev
We present a novel construction of recursion operators for scalar second-order integrable multidimensional PDEs with isospectral Lax pairs written in terms of first-order scalar di…
Extended symmetry analysis of isothermal no-slip drift flux model
Stanislav Opanasenko, Alexander Bihlo, Roman O. Popovych +1
We perform extended group analysis for a system of differential equations modeling an isothermal no-slip drift flux. The maximal Lie invariance algebra of this system is proved to…
A Simple Construction of Recursion Operators for Multidimensional Dispersionless Integrable Systems
A. Sergyeyev
We present a simple novel construction of recursion operators for integrable multidimensional dispersionless systems that admit a Lax pair whose operators are linear in the spectra…
New integrable (3+1)-dimensional systems and contact geometry
A. Sergyeyev
We introduce a novel systematic construction for integrable (3+1)-dimensional dispersionless systems using nonisospectral Lax pairs that involve contact vector fields. In particula…
On symmetries of KdV-like evolution equations
Artur Sergyeyev
The -dependence of the symmetries of (1+1)-dimensional scalar translationally invariant evolution equations is described. The sufficient condition of (quasi)polynomiality in tim…