dorsal/arxiv
View SchemaCompacton Solutions in a Class of Generalized Fifth Order Korteweg-de Vries Equations
| Authors | Fred Cooper, James M. Hyman, Avinash Khare |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9704003 |
| URL | https://arxiv.org/abs/patt-sol/9704003 |
| DOI | 10.1103/PhysRevE.64.026608 |
Abstract
We study a class of generalized fifth order Korteweg-de Vries (KdV) equations which are derivable from a Lagrangian L(p,m,n,l) which has variable powers of the first and second derivatives of the field with powers given by the parameters p,m,n,l. The resulting field equation has solitary wave solutions of both the usual (non-compact) and compact variety ("compactons"). For the particular case that p=m=n+l, the solitary wave solutions have compact support and the feature that their width is independent of the amplitude. We discuss the Hamiltonian structure of these theories and find that mass, momentum, and energy are conserved. We find in general that these are not completely integrable systems. Numerical simulations show that an arbitrary compact initial wave packet whose width is wider than that of a compacton breaks up into several compactons all having the same width. The scattering of two compactons is almost elastic, with the left over wake eventually turning into compacton-anticompacton pairs. When there are two different compacton solutions for a single set of parameters the wider solution is stable, and this solution is a minimum of the Hamiltonian.
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"abstract": "We study a class of generalized fifth order Korteweg-de Vries (KdV) equations\nwhich are derivable from a Lagrangian L(p,m,n,l) which has variable powers of\nthe first and second derivatives of the field with powers given by the\nparameters p,m,n,l. The resulting field equation has solitary wave solutions of\nboth the usual (non-compact) and compact variety (\"compactons\"). For the\nparticular case that p=m=n+l, the solitary wave solutions have compact support\nand the feature that their width is independent of the amplitude. We discuss\nthe Hamiltonian structure of these theories and find that mass, momentum, and\nenergy are conserved. We find in general that these are not completely\nintegrable systems. Numerical simulations show that an arbitrary compact\ninitial wave packet whose width is wider than that of a compacton breaks up\ninto several compactons all having the same width. The scattering of two\ncompactons is almost elastic, with the left over wake eventually turning into\ncompacton-anticompacton pairs. When there are two different compacton solutions\nfor a single set of parameters the wider solution is stable, and this solution\nis a minimum of the Hamiltonian.",
"arxiv_id": "patt-sol/9704003",
"authors": [
"Fred Cooper",
"James M. Hyman",
"Avinash Khare"
],
"categories": [
"patt-sol",
"hep-th",
"nlin.PS",
"nlin.SI",
"solv-int"
],
"doi": "10.1103/PhysRevE.64.026608",
"title": "Compacton Solutions in a Class of Generalized Fifth Order Korteweg-de Vries Equations",
"url": "https://arxiv.org/abs/patt-sol/9704003"
},
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