Related papers: The equations of some dispersionless limit
This article presents a formula for some dispersionless equations and a brief review of the operators which have been used for the dispersionless KP hierarchy.
Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these equations are integrable in the Hamiltonian…
We consider dispersionless Lax systems and present a new systematic method of deriving new integrable systems from a given one. We provide examples that include: the dispersionless Hirota equation, the general heavenly equation and the web…
Interpretation of dispersionless integrable hierarchies as equations of coisotropic deformations for certain algebras and other algebraic structures like Jordan triple systInterpretation of dispersionless integrable hierarchies as equations…
New formulae are presented for the number $P(b)$ of non-negative integer solutions of a Diophantine equation $\sum_{i=1}^{n}a_ix_i=b$ and for the number $Q(b)$ of non-negative integer solutions of the Diophantine inequality…
In this paper, we obtain a new estimate for uniform integrability under sublinear expectations. Based on this, we establish the limit theorems under nonlinear expectations dominated by sublinear expectations through tightness, and the limit…
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic…
The dispersionless limit of the scalar nonlocal dbar-problem is derived. It is given by a special class of nonlinear first-order equations. A quasi-classical version of the dbar-dressing method is presented. It is shown that the algebraic…
Using the symmetry approach, we find a class of integrable nonlinear PDEs with dispersion law $\omega(k)=k^{\frac32}$. All these equations turn out to be linearizable by means of a differential parametrization.
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
This is a write-up of the lectures on dispersionless equations in 1+1, 2+1 and 3+1 dimensions presented by one of us (RM) at "Eurasian International Center for Theoretical Physics" (EICTP). We provide pedagogical introduction to the subject…
We study equations with infinitely many derivatives. Equations of this type form a new class of equations in mathematical physics. These equations originally appeared in p-adic and later in fermionic string theories and their investigation…
A nonlinear inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can…
In this paper, several weighted summation formulas of $q$-hyperharmonic numbers are derived. As special cases, several formulas of hyperharmonic numbers of type $\sum_{\ell=1}^{n} {\ell}^{p} H_{\ell}^{(r)}$ and $\sum_{\ell=0}^{n} {\ell}^{p}…
An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media…
We give upper and lower bounds for the number of solutions of the equation $p(z)\log|z|+q(z)=0$ with polynomials $p$ and $q$.
A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions is derived by using the homogeneous balance method. With the aid of the transformation given here, exact solutions of the equations are obtained.
The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining…
Boundary value problems for linear stationary dispersive equations of order $2l+1$, $l\in \mathbb{N}$ have been considered on finite intervals $(0,L)$. The existence and uniqueness of regular solutions have been established for general…
A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of…