Modulational instability in asymmetric coupled wave functions

Ioannis Kourakis, Padma Kant Shukla

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schrödinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and the group velocity dispersion terms) and the nonlinearity and coupling coefficients, on which no assumption is made. A generalized dispersion relation is obtained, relating the frequency and wave-number of a small perturbation around a coupled monochromatic (Stokes') wave solution. Explicitly stability criteria are obtained. The analysis reveals a number of possibilities. Two (individually) stable systems may be destabilized due to coupling. Unstable systems may, when coupled, present an enhanced instability growth rate, for an extended wave number range of values. Distinct unstable wavenumber windows may arise simultaneously.
Original languageEnglish
Pages (from-to)321-325
Number of pages5
JournalEuropean Physical Journal B: Condensed Matter and Complex Systems
Volume50
Issue number1-2
DOIs
Publication statusPublished - Mar 2006

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Wave functions
wave functions
group velocity
wave dispersion
Group velocity dispersion
coupling coefficients
Stability criteria
nonlinearity
perturbation
coefficients
profiles

Cite this

Kourakis, Ioannis ; Shukla, Padma Kant. / Modulational instability in asymmetric coupled wave functions. In: European Physical Journal B: Condensed Matter and Complex Systems . 2006 ; Vol. 50, No. 1-2. pp. 321-325.
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Modulational instability in asymmetric coupled wave functions. / Kourakis, Ioannis; Shukla, Padma Kant.

In: European Physical Journal B: Condensed Matter and Complex Systems , Vol. 50, No. 1-2, 03.2006, p. 321-325.

Research output: Contribution to journalArticle

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AU - Kourakis, Ioannis

AU - Shukla, Padma Kant

PY - 2006/3

Y1 - 2006/3

N2 - The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schrödinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and the group velocity dispersion terms) and the nonlinearity and coupling coefficients, on which no assumption is made. A generalized dispersion relation is obtained, relating the frequency and wave-number of a small perturbation around a coupled monochromatic (Stokes') wave solution. Explicitly stability criteria are obtained. The analysis reveals a number of possibilities. Two (individually) stable systems may be destabilized due to coupling. Unstable systems may, when coupled, present an enhanced instability growth rate, for an extended wave number range of values. Distinct unstable wavenumber windows may arise simultaneously.

AB - The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schrödinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and the group velocity dispersion terms) and the nonlinearity and coupling coefficients, on which no assumption is made. A generalized dispersion relation is obtained, relating the frequency and wave-number of a small perturbation around a coupled monochromatic (Stokes') wave solution. Explicitly stability criteria are obtained. The analysis reveals a number of possibilities. Two (individually) stable systems may be destabilized due to coupling. Unstable systems may, when coupled, present an enhanced instability growth rate, for an extended wave number range of values. Distinct unstable wavenumber windows may arise simultaneously.

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