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We study the appearance of compacton-like solutions within the hydrodynamic-type model taking into account effects of spatial non-locality
Magneto-hydrodynamics is one of the foremost models in plasma physics with applications in inertial confinement fusion, astrophysics and elsewhere. Advanced numerical methods are needed to get an insight into the complex physical phenomena.…
Analytic-bilinear approach is used to study continuous and discrete non-isospectral symmetries of the generalized KP hierarchy. It is shown that M\"obius symmetry transformation for the singular manifold equation leads to continuous or…
We describe recent development of quantum hydrodynamics for ultracold Bose particle studying and consider different kinds of interactions. The method of derivation of equations describing the evolution of the neutral Bose particle system at…
In this work, we construct various interesting localized wave structures of the Benjamin-Ono equation describing the dynamics of deep water waves. Particularly, we extract the rogue waves and generalized breather solutions with the aid of…
Whitham modulation theory for the two dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasi-linear first-order partial differential equations is derived. The system describes modulations of the traveling wave…
We present a microscopic derivation of the nonlinear fluctuating hydrodynamic equation for the homogeneous crystalline solid from the Hamiltonian description of a many-particle system. We propose a microscopic expression of the displacement…
In the context of a nonequilibrium statistical thermodynamics, based on a nonequilibrium statistical ensemble formalism, a generalized hydrodynamics of fluids under driven flow and shear stress is derived. At the thermodynamic level, the…
Hydrodynamic equations for a binary mixture of inelastic hard spheres are derived from the Boltzmann kinetic theory. A normal solution is obtained via the Chapman-Enskog method for states near the local homogeneous cooling state. The mass,…
In this work, we study the Benjamin-Bona-Mahony like equations with a fully nonlinear dispersive term by means of the factorization technique. In this way we find the travelling wave solutions of this equation in terms of the Weierstrass…
We establish a complete set of hydrodynamic equations for a spin-1 Bose-Einstein condensate (BEC), which are equivalent to the multi-component Gross-Pitaevskii equations and expressed in terms of only observable physical quantities: the…
A systematic construction of St\"{a}ckel systems in separated coordinates and its relation to bi-Hamiltonian formalism are considered. A general form of related hydrodynamic systems, integrable by the Hamilton-Jacobi method, is derived. One…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…
Given a fluid equation with reduced Lagrangian $l$ which is a functional of velocity $\MM{u}$ and advected density $D$ given in Eulerian coordinates, we give a general method for semidiscretising the equations to give a canonical…
In this paper we study two multidimensional nonlinear dispersive systems: the Serre-Green-Naghdi (SGN) equations describing dispersive shallow water flows, and Iordanskii-Kogarko-Wijngaarden (IKW) equations describing fluids containing…
Exact solutions for laminar stratified flows of Newtonian/non-Newtonian shear-thinning fluids in horizontal and inclined channels are presented. An iterative algorithm is proposed to compute the laminar solution for the general case of a…
New Broer-Kaup type systems of hydrodynamic equations are derived from the derivative reaction-diffusion systems arising in SL(2,R) Kaup-Newell hierarchy, represented in the non-Madelung hydrodynamic form. A relation with the problem of…
Symmetry constraints for (2+1)-dimensional dispersionless integrable equations are considered. It is demonstrated that they naturally lead to systems of hydrodynamic type which arise within the reduction method. One also easily obtaines an…
A new framework is introduced for constructing interpretable and truly reliable reduced models for multiscale problems in situations without scale separation. Hydrodynamic approximation to the kinetic equation is used as an example to…
We consider a system of equations for the description of nonlinear waves in a liquid with gas bubbles. Taking into account high order terms with respect to a small parameter, we derive a new nonlinear partial differential equation for the…