Related papers: Dispersionless Limits of Some Integrable Equations
It has been argued, that in noncommutative field theories sizes of physical objects cannot be taken smaller than an elementary length related to noncommutativity parameters. By gauge-covariantly extending field equations of noncommutative…
We study the global existence of classical solutions for two-dimensional incompressible MHD system with only magnetic diffusion. By using the time-weighted lower-order energy and uniformly bounded higher-order energy estimates, we prove the…
We first derive an integrable deformed hierarchy of short pulse equation and their Lax representation. Then we concentrated on the solution of integrable deformed short pulse equation (IDSPE). By proposing a generalized reciprocal…
For several classes of second order dispersionless PDEs, we show that the symbols of their formal linearizations define conformal structures which must be Einstein-Weyl in 3D (or self-dual in 4D) if and only if the PDE is integrable by the…
In the framework of multiple-scattering theory, we show that the dispersion relations of certain electromagnetic (EM) and elastic metamaterials can be obtained analytically in the long-wavelength limit. Specific examples are given to the…
We investigate $(d+1)$-dimensional quasilinear systems which are integrable by the method of hydrodynamic reductions. In the case $d\geq 3$ we formulate a conjecture that any such system with an irreducible dispersion relation must be…
This manuscript develops a novel understanding of non-polar solutions of the discrete Painlev\'e I equation (dP1). As the non-autonomous counterpart of an analytically completely integrable difference equation, this system is endowed with a…
We consider nonlinear partial differential equations (PDEs) for advection-diffusion processes which are augmented by an auxiliary parameter $\delta$ such that $\delta=0$ corresponds to linear advection-diffusion. We derive potentially…
In this paper we investigate the zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system. We justify this singular limit rigorously in the framework of smooth solutions and obtain the non-isentropic…
These lecture notes give a pedagogical introduction to the use of dispersion relations in loop calculations. We first derive dispersion relations which allow us to recover the real part of a physical amplitude from the knowledge of its…
The paper presents the low temperature expansion of the 2D Ising model in the presence of the magnetic field in powers of $x=\exp(-J/(kT))$ and $z=\exp(B/(kT))$ with full polynomials in $z$ up to $x^{88}$ and full polynomials in $x^4$ up to…
Infinite determinantal measures introduced in this note are inductive limits of determinantal measures on an exhausting family of subsets of the phase space. Alternatively, an infinite determinantal measure can be described as a product of…
We present direct methods and symbolic software for the computation of conservation laws of nonlinear partial differential equations (PDEs) and differential-difference equations (DDEs).The methods are applied to nonlinear PDEs in (1+1)…
We discuss some formal and practical aspects related to the replacement of Integral Dispersion Relations (IDR) by derivative forms, without high-energy approximations. We first demonstrate that, for a class of functions with physical…
Completely integrable finite dimensional Hamiltonian systems are well understood thanks to the work of Liouville and Arnold. On the other hand, the Lax Pair formulation of the KdV equation marks the beginning of the extension of the…
Starting from the standard form of the five discrete Painlev\'e equations we show how one can obtain (through appropriate limits) a host of new equations which are also the discrete analogues of the continuous Painlev\'e equations. A…
The global existence of strong solutions to the compressible viscous magnetohydrodynamic (MHD) equations in $\mathbb{R}^3$ remains a significant open problem. When there is no magnetic diffusion, even small data global well-posedness is…
We are concerned with free boundary problems arising from the analysis of multidimensional transonic shock waves for the Euler equations in compressible fluid dynamics. In this expository paper, we survey some recent developments in the…
Negative-free contrastive learning methods have attracted a lot of attention with simplicity and impressive performances for large-scale pretraining. However, its disentanglement property remains unexplored. In this paper, we examine…
We study the long term evolution of magnetic fields generated by a collisionless relativistic $e^+e^-$ shock which is initially unmagnetized. Our 2D particle-in-cell numerical simulations show that downstream of such a Weibel-mediated…