Solitary waves in a class of generalized Korteweg--de Vries equations
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States) Physics Department, University of New Hampshire, Durham, New Hampshire, 03824 (United States)
- Physics Department, University of New Hampshire, Durham, New Hampshire 03824 (United States)
- Dipartimento di Fisica and Sezione INFN Universita di Perugia, 06100 Perugia (Italy)
We study the class of generalized Korteweg--de Vries (KdV) equations derivable from the Lagrangian: [ital L]([ital l],[ital p]) =[integral][1/2[ital cphi][sub [ital x]cphi[ital t]] [minus]([ital cphi][sub [ital x]])[sup [ital l]]/[ital l]([ital l][minus]1) +[alpha]([ital cphi][sub [ital x]])[sup [ital p]]([ital cphi][sub [ital x][ital x]])[sup 2]][ital dx], where the usual fields [ital u]([ital x],[ital t]) of the generalized KIdV equation are defined by [ital u]([ital x],[ital t])=[ital cphi][sub [ital x]]([ital x],[ital t]). This class contains compactons, which are solitary waves with compact support, and when [ital l]=[ital p]+2, these solutions have the feature that their width is independent of the amplitude. We consider the Hamiltonian structure and integrability properties of this class of KdV equations. We show that many of the properties of the solitary waves and compactons are easily obtained using a variational method based on the principle of least action. Using a class of trial variational functions of the form [ital u]([ital x],[ital t])=[ital A]([ital t])exp[[minus][beta]([ital t])[vert bar][ital x][minus][ital q]([ital t])[vert bar][sup 2[ital n]]] we find solitonlike solutions for all [ital n], moving with fixed shape and constant velocity, [ital c]. We show that the velocity, mass, and energy of the variational traveling-wave solutions are related by [ital c]=2[ital rEM][sup [minus]1], where [ital r]=([ital p]+[ital l]+2)/([ital p]+6[minus][ital l]), independent of [ital n].
- OSTI ID:
- 5836016
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Vol. 48:5; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
Similar Records
Compacton solutions in a class of generalized fifth-order Korteweg--de Vries equations
Compactons in PT-symmetric generalized Korteweg-de Vries equations
Related Subjects
GENERAL PHYSICS
KORTEWEG-DE VRIES EQUATION
SOLITONS
AMPLITUDES
HAMILTONIANS
LAGRANGIAN FUNCTION
VARIATIONAL METHODS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
QUASI PARTICLES
661100* - Classical & Quantum Mechanics- (1992-)