dorsal/arxiv
View SchemaContinuous vacua in bilinear soliton equations
| Authors | J. Hietarinta, A. Ramani, B. Grammaticos |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9311001 |
| URL | https://arxiv.org/abs/solv-int/9311001 |
| DOI | 10.1088/0305-4470/27/9/027 |
Abstract
We discuss the freedom in the background field (vacuum) on top of which the solitons are built. If the Hirota bilinear form of a soliton equation is given by $A(D_{\vec x})\bd GF=0,\, B(D_{\vec x})(\bd FF - \bd GG)=0$ where both $A$ and $B$ are even polynomials in their variables, then there can be a continuum of vacua, parametrized by a vacuum angle $\phi$. The ramifications of this freedom on the construction of one- and two-soliton solutions are discussed. We find, e.g., that once the angle $\phi$ is fixed and we choose $u=\arctan G/F$ as the physical quantity, then there are four different solitons (or kinks) connecting the vacuum angles $\pm\phi$, $\pm\phi\pm\Pi2$ (defined modulo $\pi$). The most interesting result is the existence of a ``ghost'' soliton; it goes over to the vacuum in isolation, but interacts with ``normal'' solitons by giving them a finite phase shift.
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"abstract": "We discuss the freedom in the background field (vacuum) on top of which the\nsolitons are built. If the Hirota bilinear form of a soliton equation is given\nby $A(D_{\\vec x})\\bd GF=0,\\, B(D_{\\vec x})(\\bd FF - \\bd GG)=0$ where both $A$\nand $B$ are even polynomials in their variables, then there can be a continuum\nof vacua, parametrized by a vacuum angle $\\phi$. The ramifications of this\nfreedom on the construction of one- and two-soliton solutions are discussed. We\nfind, e.g., that once the angle $\\phi$ is fixed and we choose $u=\\arctan G/F$\nas the physical quantity, then there are four different solitons (or kinks)\nconnecting the vacuum angles $\\pm\\phi$, $\\pm\\phi\\pm\\Pi2$ (defined modulo\n$\\pi$). The most interesting result is the existence of a ``ghost\u0027\u0027 soliton; it\ngoes over to the vacuum in isolation, but interacts with ``normal\u0027\u0027 solitons by\ngiving them a finite phase shift.",
"arxiv_id": "solv-int/9311001",
"authors": [
"J. Hietarinta",
"A. Ramani",
"B. Grammaticos"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1088/0305-4470/27/9/027",
"title": "Continuous vacua in bilinear soliton equations",
"url": "https://arxiv.org/abs/solv-int/9311001"
},
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