Fully nonlinear solitary waves in a dusty electronegative multispecies plasmas

Abstract. The presence of dynamic, large amplitude solitary waves in the auroral regions of space is well known. Since their velocities are of the order of the ion acoustic speed, they may well be considered as being generated from the nonlinear evolution of ion acoustic waves. However, they do not show the expected width-amplitude correlation for K-dV solitons. Recent POLAR observations have actually revealed that the low altitude rarefactive ion acoustic solitary waves are associated with an increase in the width with increasing amplitude. This indicates that a weakly nonlinear theory is not appropriate to describe the solitary structures in the auroral regions. In the present work, a fully nonlinear analysis based on Sagdeev pseudopotential technique has been adopted for both parallel and oblique propagation of rarefactive solitary waves in a two electron temperature multi-ion plasma. The large amplitude solutions have consistently shown an increase in the width with increasing amplitude. The width-amplitude variation profile of obliquely propagating rarefactive solitary waves in a magnetized plasma have been compared with the recent POLAR observations. The width-amplitude variation pattern is found to fit well with the analytical results. It indicates that a fully nonlinear theory of ion acoustic solitary waves may well explain the observed anomalous width variations of large amplitude structures in the auroral region.

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Fully Nonlinear Model for Simulating Solitary Waves Propagating through a Partially Immersed Rectangular Structure

Journal of Coastal Research ◽

10.2112/jcoastres-d-16-00061.1 ◽

2017 ◽

Vol 336 ◽

pp. 1487-1497

Author(s):

Chih-Hua Chang ◽

Keh-Han Wang ◽

Ping-Cheng Hsieh

Keyword(s):

Solitary Waves ◽

Nonlinear Model ◽

Fully Nonlinear

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The Use of Nonlinear Solitary Waves for Computing Short Wave Equation Pulses

Mathematical and Numerical Aspects of Wave Propagation WAVES 2003 ◽

10.1007/978-3-642-55856-6_127 ◽

2003 ◽

pp. 782-787

Author(s):

John Steinhoff ◽

Meng Fan ◽

Lesong Wang ◽

Min Xiao

Keyword(s):

Wave Equation ◽

Solitary Waves ◽

Short Wave ◽

Nonlinear Solitary Waves

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The transformation of an interfacial solitary wave of elevation at a bottom step

Nonlinear Processes in Geophysics ◽

10.5194/npg-16-33-2009 ◽

2009 ◽

Vol 16 (1) ◽

pp. 33-42 ◽

Cited By ~ 23

Author(s):

V. Maderich ◽

T. Talipova ◽

R. Grimshaw ◽

E. Pelinovsky ◽

B. H. Choi ◽

...

Keyword(s):

Solitary Wave ◽

Solitary Waves ◽

Numerical Study ◽

Nonlinear Effects ◽

Ocean Model ◽

Gardner Equation ◽

Fully Nonlinear ◽

Layer Flow ◽

The One ◽

Bottom Step

Abstract. In this paper we study the transformation of an internal solitary wave at a bottom step in the framework of two-layer flow, for the case when the interface lies close to the bottom, and so the solitary waves are elevation waves. The outcome is the formation of solitary waves and dispersive wave trains in both the reflected and transmitted fields. We use a two-pronged approach, based on numerical simulations of the fully nonlinear equations using a version of the Princeton Ocean Model on the one hand, and a theoretical and numerical study of the Gardner equation on the other hand. In the numerical experiments, the ratio of the initial wave amplitude to the layer thickness is varied up one-half, and nonlinear effects are then essential. In general, the characteristics of the generated solitary waves obtained in the fully nonlinear simulations are in reasonable agreement with the predictions of our theoretical model, which is based on matching linear shallow-water theory in the vicinity of a step with solutions of the Gardner equation for waves far from the step.

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