Introducing envelope soliton solutions for wave–structure investigations

2021 ◽  
Vol 234 ◽  
pp. 109271
Author(s):  
Marco Klein ◽  
Günther F. Clauss ◽  
Norbert Hoffmann
Keyword(s):  
Soliton Solutions ◽  
Wave Structure ◽  
Envelope Soliton ◽  
Structure Investigations

scholarly journals Properties of Alfvén Solitons in a Finite-Beta Plasma J. Plasma Phys. vol. 27, 1982, p. 193

1984 ◽  
Vol 32 (2) ◽  
pp. 347-347 ◽  
Author(s):  
Steven R. Spangler ◽  
James P. Sheerin
Keyword(s):  
Soliton Solutions ◽  
Alfven Waves ◽  
Plasma Phys ◽  
Alfvén Waves ◽  
Envelope Soliton ◽  
Translational Invariance ◽  
Non Linear ◽  
Image Position

In the aforementioned paper we obtained an equation for non-linear Alfvén waves in a finite-β plasma, and investigated envelope soliton solutions thereof. The purpose of this note is to point out an error in the derivation of the soliton envelopes, and present corrected expressions for these solitons.The error arises from our assumption of translational invariance of both the envelope and phase of an envelope soliton expressed in equations (16) and (17). Rather, the phase is related to the amplitude by where y ≡ x — VEt is a comoving co-ordinate, and all other quantities are defined in the above paper.

INTEGRABLE ASPECTS AND SOLITON-LIKE SOLUTIONS OF AN INHOMOGENEOUS COUPLED HIROTA–MAXWELL–BLOCH SYSTEM IN OPTICAL FIBERS WITH SYMBOLIC COMPUTATION

2010 ◽  
Vol 25 (16) ◽  
pp. 1365-1381 ◽  
Author(s):  
YU-SHAN XUE ◽  
BO TIAN ◽  
HAI-QIANG ZHANG ◽  
LI-LI LI
Keyword(s):  
Symbolic Computation ◽  
Optical Fibers ◽  
Soliton Solutions ◽  
Graphical Analysis ◽  
Envelope Soliton ◽  
Fiber Communication ◽  
Erbium Doped ◽  
Higher Order Dispersion ◽  
Interaction Behaviors ◽  
Soliton Excitation

For describing wave propagation in an inhomogeneous erbium-doped nonlinear fiber with higher-order dispersion and self-steepening, an inhomogeneous coupled Hirota–Maxwell–Bloch system is considered with the aid of symbolic computation. Through Painlevé singularity structure analysis, the integrable condition of such a system is analyzed. Via the Painlevé-integrable condition, the Lax pair is explicitly constructed based on the Ablowitz–Kaup–Newell–Segur scheme. Furthermore, the analytic soliton-like solutions are obtained via the Darboux transformation which makes it exercisable to generate the multi-soliton solutions in a recursive manner. Through the graphical analysis of some obtained analytic one- and two-soliton-like solutions, our concerns are mainly on the envelope soliton excitation, the propagation features of optical solitons and their interaction behaviors in actual fiber communication. Finally, the conservation laws for the system are also presented.

Evolution theorem for a class of perturbed envelope soliton solutions

1983 ◽  
Vol 24 (12) ◽  
pp. 2764-2769 ◽  
Author(s):  
E. W. Laedke ◽  
K. H. Spatschek ◽  
L. Stenflo
Keyword(s):  
Soliton Solutions ◽  
Envelope Soliton

The effect of the induced mean flow on solitary waves in deep water

1998 ◽  
Vol 355 ◽  
pp. 317-328 ◽  
Author(s):  
T. R. AKYLAS ◽  
F. DIAS ◽  
R. H. J. GRIMSHAW
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Deep Water ◽  
Water Waves ◽  
Wave Equations ◽  
Soliton Solutions ◽  
Phase Speed ◽  
Mean Flow ◽  
Nls Equation ◽  
Envelope Soliton

Two branches of gravity–capillary solitary water waves are known to bifurcate from a train of infinitesimal periodic waves at the minimum value of the phase speed. In general, these solitary waves feature oscillatory tails with exponentially decaying amplitude and, in the small-amplitude limit, they may be interpreted as envelope-soliton solutions of the nonlinear Schrödinger (NLS) equation such that the envelope travels at the same speed as the carrier oscillations. On water of infinite depth, however, based on the fourth-order envelope equation derived by Hogan (1985), it is shown that the profile of these gravity–capillary solitary waves actually decays algebraically (like 1/x2) at infinity owing to the induced mean flow that is not accounted for in the NLS equation. The algebraic decay of the solitary-wave tails in deep water is confirmed by numerical computations based on the full water-wave equations. Moreover, the same behaviour is found at the tails of solitary-wave solutions of the model equation proposed by Benjamin (1992) for interfacial waves in a two-fluid system.

Long-living coherent patterns in the fields of irregular waves in deep water

2021 ◽  
Author(s):  
Alexey Slunyaev ◽  
Anna Kokorina
Keyword(s):  
Numerical Simulations ◽  
Deep Water ◽  
Water Waves ◽  
Rogue Wave ◽  
Scattering Problem ◽  
Wave Structure ◽  
Irregular Waves ◽  
Envelope Soliton ◽  
Coherent Wave ◽  
Wave Patterns

<p>Long-living coherent wave patterns embedded into the irregular wave fields are studied using the data of extensive numerical simulations of the Euler equations in deep water. The distributions of the rogue wave lifetimes according to the numerical simulations of JONSWAP waves with narrow and broad angle spectra are discussed. The observation of a wave group persisting for more than 200 periods in the direct numerical simulation of nonlinear unidirectional irregular water waves is discussed. Through solution of the associated scattering problem for the nonlinear Schrodinger equation, the persisting group is identified as the intense envelope soliton with remarkably stable parameters. Most of extreme waves occur on top of this group, resulting in higher and longer rogue wave events. It is shown that the persisting wave structure survives under the conditions of directional waves with moderate spread of directions. The survivability of coherent wave patterns is expected to further increase when the waves are guided by currents or the topography.</p><p> </p><p>The research is supported by the RSF grant No. 19-12-00253; the study of trapped waves is performed for the RFBR grant No. 21-55-15008.</p>

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