One-parameter family of soliton solutions with compact support in a class of generalized Korteweg--de Vries equations

Journal Article · Wed Dec 01 04:00:00 EST 1993 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.48.4843· OSTI ID:5723811

Khare, A ^[1]; Cooper, F ^[2]

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1. Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States) Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005 (India)
2. Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

We study the 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 KdV equation are defined by [ital u]([ital x],[ital t])=[ital cphi][sub [ital x]]([ital x],[ital t]). For [ital p] an arbitrary continuous parameter 0[lt][ital p][le]2, [ital l]=[ital p]+2 we find soliton solutions with compact support (compactons) to these equations which have the feature that their width is independent of the amplitude. This generalizes previous results which considered [ital p]=1,2. For the exact compactons we find a relation between the energy, mass, and velocity of the solitons. We show that this relationship can also be obtained using a variational method based on the principle of least action.

• OSTI ID: 5723811
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 48:6; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

665000* -- Physics of Condensed Matter-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANALYTICAL SOLUTION
DIFFERENTIAL EQUATIONS
ENERGY
EQUATIONS
FUNCTIONS
KORTEWEG-DE VRIES EQUATION
LAGRANGIAN FUNCTION
MASS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
QUASI PARTICLES
SELF-ENERGY
SOLITONS
VELOCITY
WAVE FUNCTIONS