Interactions of Solitary Waves –A Perturbation Approach to Nonlinear Systems–

Oikawa, Masayuki; Yajima, Nobuo

doi:10.1143/jpsj.34.1093

Cited by 86 publications

(47 citation statements)

References 11 publications

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“…To evaluate the dynamics of this collision, we use asymptotic expansion of plasma variables around thermodynamics equilibrium state in an appropriate strained coordinate which contains the phase records of each wave. The technique is the so-called extended Poincaré-Lighthill-Kuo (PLK) method [39,40]. The reductive perturbation method in nonlinear wave propagation has been put forward by Taniuti and Wei [41], where it was shown that the stretching of ξ = ε a (x − ct), τ = ε a+1 and a = ( p − 1) −1 with p = 2, p = 3 admit reductions to Burgers and KdV equations, respectively.…”

Section: Qhd Description Of Plasmamentioning

confidence: 99%

“…It has been shown [44] that, the method of multiple scales combined with the reductive perturbation technique, not only eliminates the secularities arising in the second-order correction but also modifies the phase factor of the lowest KdV soliton proportional to its amplitude. A fuller discussion of the elimination of secularities in higher-order amplitude approximation is given in [40]. From the latter requirement the phase-shifts introduced in eqs (8) are derived.…”

Section: Solitary Collision Dynamicsmentioning

confidence: 99%

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Propagation and oblique collision of electron-acoustic solitons in two-electron-populated quantum plasmas

Akbari-Moghanjoughi

Ahmadzadeh-Khosroshahi²

2011

Pramana - J Phys

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Oblique interaction of small-but finite-amplitude KdV-type electron-acoustic solitary excitations is examined in an unmagnetized two-electron-populated degenerate quantum electron-ion plasma in the framework of quantum hydrodynamics model using the extended Poincaré-LighthillKuo (PLK) perturbation method. Critical plasma parameter is found to distinguish the types of solitons and their interaction phase-shifts. It is shown that, depending on the critical quantum diffraction parameter H cr , both compressive and rarefactive solitary excitations may exist in this plasma and their collision phase-shifts can be either positive or negative for the whole range of collision angles 0 < θ < π.

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Section: Qhd Description Of Plasmamentioning

confidence: 99%

Section: Solitary Collision Dynamicsmentioning

confidence: 99%

Propagation and oblique collision of electron-acoustic solitons in two-electron-populated quantum plasmas

Akbari-Moghanjoughi

Ahmadzadeh-Khosroshahi²

2011

Pramana - J Phys

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“…The phase shift is computed at an instant of time much larger than t d to consider a wave travelling unaffected by the presence of the wall. Oikawa and Yajima (1973) explicitly computed the spatial phase shift x incurred after reflection from the wall, namely: …”

Section: Phase Shiftmentioning

confidence: 99%

“…This loss of amplitude is due to the presence of the third-order dispersive tail. Oikawa and Yajima (1973) used a singular perturbation method developed to secondorder to study the interaction between two solitary waves which propagate in opposite directions. They provided an estimate of the phase shifts in the collision process of the two solitary waves.…”

Section: Introductionmentioning

confidence: 99%

Head-on collision of two solitary waves and residual falling jet formation

Chambarel

Kharif

Touboul

2009

Nonlin. Processes Geophys.

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Abstract. The head-on collision of two equal and two unequal steep solitary waves is investigated numerically. The former case is equivalent to the reflection of one solitary wave by a vertical wall when viscosity is neglected. We have performed a series of numerical simulations based on a Boundary Integral Equation Method (BIEM) on finite depth to investigate during the collision the maximum runup, phase shift, wall residence time and acceleration field for arbitrary values of the non-linearity parameter a/h, where a is the amplitude of initial solitary waves and h the constant water depth. The initial solitary waves are calculated numerically from the fully nonlinear equations. The present work extends previous results on the runup and wall residence time calculation to the collision of very steep counter propagating solitary waves. Furthermore, a new phenomenon corresponding to the occurrence of a residual jet is found for wave amplitudes larger than a threshold value.

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“…Several different approaches are known at present. These include a method based on the inverse-scattering transform (IST) [12 -16], a direct method using multiple-time-scale expansion [17 -20], a mixture of the above two methods [21 -24], a technique using the variational principle [25], and a generalized reductive perturbation method [5,6,26]. These methods are reviewed critically in the literature [27,28] and hence their advantages are not discussed here.…”

Section: Introductionmentioning

confidence: 99%

Multisoliton perturbation theory for the Benjamin-Ono equation and its application to real physical systems

Matsuno

1995

Phys. Rev. E

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A direct perturbation theory is developed to study the effects of small perturbations on the interaction process of algebraic solitons of the Benjamin-Ono (BO) equation. Using the method of multiple scales, the modulation equations for the amplitude and the phase of each soliton are derived in the lowest approximation. As practical applications of the theory, the interaction of two solitons is investigated for the two different types of perturbations that appear in real physical systems. One is a dissipative perturbation (BO -Burgers equation) and the other is a dispersive perturbation (higher-order BO equation). In both cases, the changes of the soliton parameters due to small perturbation are calculated by numerical integrations and their characteristics are elucidated in detail. Among them, the phase shift caused by the dispersive perturbation is a remarkable feature that has never been observed in the collision process of algebraic solitons.

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Interactions of Solitary Waves –A Perturbation Approach to Nonlinear Systems–

Cited by 86 publications

References 11 publications

Propagation and oblique collision of electron-acoustic solitons in two-electron-populated quantum plasmas

Propagation and oblique collision of electron-acoustic solitons in two-electron-populated quantum plasmas

Head-on collision of two solitary waves and residual falling jet formation

Multisoliton perturbation theory for the Benjamin-Ono equation and its application to real physical systems

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