By N. Akhmediev, A. Ankiewicz (auth.), Adrian Ankiewicz, Nail Akhmediev (eds.)
The dissipative soliton inspiration is a basic extension of the concept that of solitons in conservative and integrable platforms. It comprises principles from 3 significant resources, specifically ordinary soliton thought constructed because the Sixties, nonlinear dynamics concept, and Prigogine's rules of platforms faraway from equilibrium. those 3 resources additionally correspond to the 3 part components of this novel paradigm. This publication explains the above ideas intimately and provides the reader a variety of examples from optics, biology and medication. those comprise laser platforms, optical transmission strains, cortical networks, versions of muscle contraction, localized crops buildings and waves in mind tissues.
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Additional resources for Dissipative solitons: from optics to biology and medicine
As regards Fig. 14b, we have c0 < 0 in the lower right hand corner region (low energy Q0 ), while we find c0 > 0 in the upper left corner region (high energy Q0 ). The same patterns for the chirp signs are obtained in the two distinct regions in Fig. 15a and b when directly solving the CGLE. 1 1 0 −4 0 x 4 0 0 −5 0 x 5 0 Fig. 16 Exact soliton profiles (solid lines) of two examples in the (a) upper and (b) lower regions in Fig. 15b. They are marked by thick black dots in Fig. 15b. Dashed lines show their corresponding phase profiles 24 N.
The full system of long-wave equations which describes Solitons in Viscous Flows 39 such waves is rather complicated (see ). , dissipative solitons at arbitrary incident angles. , a phase shift) whose value is proportional to sin2 ψ∗ − 1, sin2 ψ 1 Mc sin2 ψ∗ = 3− 4 G + Mc Ψ= (45) . (46) For a given experiment, the change of sign of the phase shift takes place at the “critical” angle ψ = ψ∗ . Wider angles than the critical value yield a Mach–Russell third wave or stem. In the limit G Mc = 12, the result of Miles  for interacting solitons in ideal, viscous-free shallow liquid layers, ψ∗ → π /3, is recovered.
There are some obvious differences in the energies, widths and amplitudes of the two solitons. However, the most visible qualitative difference is in the soliton chirp. The phase profiles clearly show that the chirps in the two cases are of opposite signs. Due to this difference, the energy flows from the inside to the outside of the soliton in the first case while it flows inwards in the second case. The results obtained from the finite dimensional model (11) show that, for Fig. , there is a strong chirp across the soliton.