Quasicollapse of oblique solitons of the weakly dissipative derivative nonlinear Schroedinger equation

Journal Article · Thu Jul 15 04:00:00 EDT 2010 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.82.016406· OSTI ID:21362190

Sanchez-Arriaga, G; Laveder, D; Passot, T; Sulem, P L ^[1]

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1. Departamento de Fisica Aplicada, Escuela Tecnica Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Plaza de Cardenal Cisneros 3, 28040 Madrid (Spain)

Numerical integrations of the derivative nonlinear Schroedinger equation for Alfven waves, supplemented by a weak dissipative term (originating from diffusion or Landau damping), with initial conditions in the form of a bright soliton with nonvanishing conditions at infinity (oblique soliton), reveal an interesting phenomenon of 'quasicollapse': as the dissipation parameter is reduced, larger amplitudes are reached and smaller scales are created, but on an increasing time scale. This process involves an early bifurcation of the initial soliton toward a breather that is analyzed by means of a numerical inverse scattering technique. This evolution leads to the formation of persistent dark solitons that are only weakly affected when crossed by the decaying breather which has the form of either a localized structure or an extended wave packet.

• OSTI ID: 21362190
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print) Journal Issue: 1 Vol. 82; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ALFVEN WAVES
BIFURCATION
DAMPING
DIFFERENTIAL EQUATIONS
EQUATIONS
EVOLUTION
HYDROMAGNETIC WAVES
INVERSE SCATTERING PROBLEM
LANDAU DAMPING
MATHEMATICAL EVOLUTION
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
QUASI PARTICLES
SCHROEDINGER EQUATION
SOLITONS
WAVE EQUATIONS
WAVE PACKETS