Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2005-02-10
Nonlinear Sciences
Pattern Formation and Solitons
6 pages, the figure has been removed and it has been explaind that the antisymmetric solutions are everywhere valid within the
Scientific paper
The origin of 1D spirals or antisymmetric 1D pulses is explaind so far on the basis of multistability of spatially inhomogeneous and temporally oscillatory phases and so called nonvariational effects. Thus, coupled amplitude equations which are valid near a co-dimention 2 point and provides with the necessary multistable environment are commonly in use in the numerical calculations to generate such structures. In the present work we analytically show that a complex Ginzburg-Landau type amplitude equation which is valid in the Hopf region of phase space near an instability threshold admits solutions like antisymmetric pulses traveling in alternate directions from a core. The pulses can have well defined spatial profile like Hermite polynomial of order unity on the side of the direction of its motion. Thus, a pulse moving in the positive direction of x-axis from near a core at origin will be a peak while that moving in the negative direction is a trough and a temporal oscillation of such structures would give the impression of alternative peak and troughs are moving appart being generated from a common core.
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