dorsal/arxiv
View SchemaConservation Laws in Field Dynamics or Why Boundary Motion is Exactly Integrable?
| Authors | Mark B. Mineev-Weinstein |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9501004 |
| URL | https://arxiv.org/abs/solv-int/9501004 |
Abstract
An infinite number of conserved quantities in the field dynamics $\phi_t = L U(\phi) + \rho$ for a linear Hermitian (or anti-Hermitian) operator $L$, an arbitrary function $U$ and a given source $\rho$ are presented. These integrals of motion are the multipole moments of the potential created by $\phi$ in the far-field. In the singular limit of a bistable scalar field $\phi = \phi_{\pm}$ (i.e. Ising limit) this theory describes a dissipative boundary motion (such as Stefan or Saffman-Taylor problem that is the continuous limit of the DLA-fractal growth) and can be exactly integrable. These conserved quantities are the polynomial conservation laws attributed to the integrability. The criterion for integrability is the uniqueness of the inverse potential problem's solution.
{
"annotation_id": "ab74629d-9b1d-487e-b756-6fe4533bc492",
"date_created": "2026-03-02T18:02:48.369000Z",
"date_modified": "2026-03-02T18:02:48.369000Z",
"file_hash": "25c7c9d626dc940932b4af52e28c0083d0dea79885e509cdb67cb83848e4c5e0",
"private": false,
"record": {
"abstract": "An infinite number of conserved quantities in the field dynamics $\\phi_t = L\nU(\\phi) + \\rho$ for a linear Hermitian (or anti-Hermitian) operator $L$, an\narbitrary function $U$ and a given source $\\rho$ are presented. These integrals\nof motion are the multipole moments of the potential created by $\\phi$ in the\nfar-field. In the singular limit of a bistable scalar field $\\phi = \\phi_{\\pm}$\n(i.e. Ising limit) this theory describes a dissipative boundary motion (such as\nStefan or Saffman-Taylor problem that is the continuous limit of the\nDLA-fractal growth) and can be exactly integrable. These conserved quantities\nare the polynomial conservation laws attributed to the integrability. The\ncriterion for integrability is the uniqueness of the inverse potential\nproblem\u0027s solution.",
"arxiv_id": "solv-int/9501004",
"authors": [
"Mark B. Mineev-Weinstein"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Conservation Laws in Field Dynamics or Why Boundary Motion is Exactly Integrable?",
"url": "https://arxiv.org/abs/solv-int/9501004"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "5ca21379-d3b4-44fb-9df7-133662a63393",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}