dorsal/arxiv
View SchemaContinuum limit of nonlinear discrete systems with long range interaction potentials
| Authors | A. S. Cârstea, D. Grecu, A. Visinescu |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9707016 |
| URL | https://arxiv.org/abs/solv-int/9707016 |
Abstract
One dimensional nonlinear lattices with harmonic long range interaction potentials (LRIP) having an inverse power kernel type, are studied. For the nearest neighbour nonlinear interaction we consider the anharmonic potential of the Fermi-Pasta-Ulam problem and the \phi^3+\phi^4 potential as well. The continuum limit is obtained following the method used by Ishimori and several Boussinesq and KdV type equations with supplementary Hilbert transform terms are found. These nonlocal terms are introduced by the LRIP. For the \phi^3+\phi^4 nearest neighbour interactions the continuum approximation turns out to admit exact bilinearization in Hirota formalism. Exact rational nonsingular solutions are found. The integrability of these nonlocal equations and the connection with perturbed KdV are also discussed.
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"abstract": "One dimensional nonlinear lattices with harmonic long range interaction\npotentials (LRIP) having an inverse power kernel type, are studied. For the\nnearest neighbour nonlinear interaction we consider the anharmonic potential of\nthe Fermi-Pasta-Ulam problem and the \\phi^3+\\phi^4 potential as well. The\ncontinuum limit is obtained following the method used by Ishimori and several\nBoussinesq and KdV type equations with supplementary Hilbert transform terms\nare found. These nonlocal terms are introduced by the LRIP. For the\n\\phi^3+\\phi^4 nearest neighbour interactions the continuum approximation turns\nout to admit exact bilinearization in Hirota formalism. Exact rational\nnonsingular solutions are found. The integrability of these nonlocal equations\nand the connection with perturbed KdV are also discussed.",
"arxiv_id": "solv-int/9707016",
"authors": [
"A. S. C\u00e2rstea",
"D. Grecu",
"A. Visinescu"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Continuum limit of nonlinear discrete systems with long range interaction potentials",
"url": "https://arxiv.org/abs/solv-int/9707016"
},
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