Abstract
A simple one‐dimensional non linear equation including effects of instability, dissipation, and dispersion is examined numerically. Periodic solution of a non linear dispersive equation is presented for different values of α, β, and γ characterizing the constants for instability, dissipation, and dispersion respectively. In this paper, the growth pattern for the wave at different time intervals is discussed. Various equilibrium states with different initial configuration have been observed depending on initial conditions.
Highlights
1.0 INTRODUCTION One of the intrinsic properties attributed to dispersion in a non linear system with instability and dissipation has been pointed out by a numerical initial value problem concerning a simple one-dimensional model equation [1], given by: Dispersion works as an effective impedance in non linear mode coupling processes and results in saturation at higher amplitudes for strong dispersion leading to a non linear equilibrium, i.e., a row of saturated soliton like pulses
It is interesting to notice from the linear dispersion relation, f2 txk y k + il3k which is obtained by substitution ofU exp(ikx + Qt) into the linear version of Equation-I, small amplitude sinusoidal waves with long wavelengths are linearly unstable
One ofthe simplest non-linear effects which is capable of saturating the growth of a linearly unstable wave or spectrum of waves is resonant mode coupling [6]
Summary
One of the intrinsic properties attributed to dispersion in a non linear system with instability and dissipation has been pointed out by a numerical initial value problem concerning a simple one-dimensional model equation [1], given by: Dispersion works as an effective impedance in non linear mode coupling processes and results in saturation at higher amplitudes for strong dispersion leading to a non linear equilibrium, i.e., a row of saturated soliton like pulses. 1.0 INTRODUCTION One of the intrinsic properties attributed to dispersion in a non linear system with instability and dissipation has been pointed out by a numerical initial value problem concerning a simple one-dimensional model equation [1], given by: Dispersion works as an effective impedance in non linear mode coupling processes and results in saturation at higher amplitudes for strong dispersion leading to a non linear equilibrium, i.e., a row of saturated soliton like pulses.
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