Related papers: Loewner equations and dispersionless hierarchies
In this paper we are concerned with the existence of segregated non-radial solutions for nonlinear Schr\"odinger systems with a large number of components in a weak fully attractive or repulsive regime in presence of a suitable external…
We study linear dispersive equations in dimension one and two for a class of radial nonhomogeneous phases. L 1 $\rightarrow$ L $\infty$ type estimates, Strichartz estimates, local Kato smoothing and Morawetz type estimates are provided. We…
B.A. Dubrovin proved that remarkable WDVV associativity equations are integrable systems. In a simplest nontrivial three-component case these equations can be written as a nondiagonalizable hydrodynamic type system equivalent to a symmetric…
We introduce a collection of nonlinear integrable partial differential-difference equations that are satisfied by the one-point distribution functions of some classical integrable KPZ models. Moreover, these equations can be regarded as…
In the present paper initial problems for the semilinear integro-differential diffusion equation and system are considered. The analogue of Duhamel principle for the linear integro-differential diffusion equation is proved. The results on…
We develop the theory of Whitham type hierarchies integrable by hydrodynamic reductions as a theory of certain differential-geometric objects. As an application we construct Gibbons-Tsarev systems associated to moduli space of algebraic…
An overview of Hamiltonian systems with noncanonical Poisson structures is given. Examples of bi-Hamiltonian ode's, pde's and lattice equations are presented. Numerical integrators using generating functions, Hamiltonian splitting,…
In this paper we consider a reduction of a non-homogeneous linear system of first order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant…
We consider the Rosenau equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solution of the Burgers equation.…
Structure-preserving linearly implicit exponential integrators are constructed for Hamiltonian partial differential equations with linear constant damping. Linearly implicit integrators are derived by polarizing the polynomial terms of the…
The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite 2D channel.…
Dispersionless Hirota type equations are extracted from the dispersionless limit of the Fay differential identity due to Takasaki- Takebe. A few other results are sketched between inverse scattering, dKdV, and gravity.
We study the underlying relationship between Painleve equations and infinite-dimensional integrable systems, such as the KP and UC hierarchies. We show that a certain reduction of these hierarchies by requiring homogeneity and periodicity…
In the series of recent publications we have proposed a novel approach to the classification of integrable differential/difference equations in 3D based on the requirement that hydrodynamic reductions of the corresponding dispersionless…
This paper is concerned with the Becker-D\"{o}ring (BD) system of equations and their relationship to the Lifschitz-Slyozov-Wagner (LSW) equations. A diffusive version of the LSW equations is derived from the BD equations. Existence and…
The Dirichlet problem for a class of quasilinear elliptic systems of equations with small-BMO coefficients in Reifenberg-flat domain is considered. The lower order terms supposed to satisfy controlled growth conditions. It is obtained…
We investigate dispersionless integrable systems in 3D associated with fourfolds in the Grassmannian Gr(3,5). Such systems appear in numerous applications in continuum mechanics, general relativity and differential geometry, and include…
The factorization problem of the multi-component 2D Toda hierarchy is used to analyze the dispersionless limit of this hierarchy. A dispersive version of the Whitham hierarchy defined in terms of scalar Lax and Orlov--Schulman operators is…
The Darboux transformation on matrix solutions to the generalized coupled dispersionless integrable system based on some non-abelian Lie group, is studied and the solutions are shown to be expressed in terms of quasideterminants. As an…
New extensions of the KP and modified KP hierarchies with self-consistent sources are proposed. The latter provide new generalizations of $(2+1)$-dimensional integrable equations, including the DS-III equation and the $N$-wave problem.…