Reductive Perturbation Method in Nonlinear Wave Propagation. I

Taniuti, Tosiya; Wei, Chau‐Chin

doi:10.1143/jpsj.24.941

Cited by 521 publications

(169 citation statements)

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“…The quadratic steepening parameters for arbitrary values of the coefficient of thermal expansion ͑1͒ were derived through use of the multiple scales technique of Taniuti and Wei. 3 The exact results for first and second sound are given in equations ͑49͒ and ͑50͒, respectively. The corresponding results in terms of density and entropy ͑rather than pressure and temperature͒ derivatives are given in ͑44͒ and ͑45͒.…”

Section: Discussionmentioning

confidence: 99%

“…Nonlinear effects will be taken into account by applying the well-known multiple scales technique of Taniuti and Wei. 3 The governing equations will be taken to be the Landau two-fluid equations, the exact form of which are given in Section II. The general a͒ Telephone: ϩ43 1 58801 4505; Fax: ϩ43 1 5878904; Electronic mail: akluwick@hp.fluid.tuwien.ac.at multiple-scales approach is described in Section III A and the linear theory is examined in Sections III B-III C. In Section III C we show that even the linear theory is inaccurate if the ␤ϭ0 approximation is applied universally to problems involving first sound.…”

Section: ϫ2mentioning

confidence: 99%

“…To derive the evolution equation we follow the reductive perturbation method introduced by Taniuti and Wei, 3 assuming that cumulative nonlinear effects are of importance at times of O(1/␦). Transformation from (x,t) to a wave coordinate XϭxϪ t, where is the linear sound speed of the propagation mode under consideration, and a slow time scale ϭ␦t then finally shows that the evolution of small disturbances is governed by an inviscid Burgers equation:…”

Section: A Outline Of Derivationmentioning

confidence: 99%

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The effect of thermal expansion on nonlinear first and second sound in the whole temperature region of He II

1996

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We consider one-dimensional, weakly nonlinear first and second sound waves in He II. The first correction to the shock speed is computed for each sound mode. The expressions obtained are exact with respect to the coefficient of thermal expansion ␤. It is shown that the commonly made assumption of negligible ␤ can lead to significant error in the shock speeds for first sound away from the lambda-line. This contrasts with the calculation of the linear sound speeds and the shock speed for second sound where the ␤ϭ0 approximation yields accurate results. Near the lambda-line, the exact expressions for both modes are seen to contain fundamentally different singularities than those found in the commonly employed ␤ϭ0 theory.

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Section: Discussionmentioning

confidence: 99%

Section: ϫ2mentioning

confidence: 99%

Section: A Outline Of Derivationmentioning

confidence: 99%

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The effect of thermal expansion on nonlinear first and second sound in the whole temperature region of He II

1996

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“…11 and 12͒. This method is a generalization of the reductive perturbation method [13][14][15][16] for nonlinear waves propagating in random media. Following Gurevich et al, 10 we introduce the running variable,…”

Section: Derivation Of the Governing Equationmentioning

confidence: 99%

Propagation of solitons of the Derivative Nonlinear Schrödinger equation in a plasma with fluctuating density

Рудерман¹

2002

Physics of Plasmas

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The propagation of quasi-parallel nonlinear small-amplitude magnetohydrodynamic waves in a cold Hall plasma with fluctuating density is studied. The density is assumed to be a homogeneous random function of one spatial variable. The modified Derivative Nonlinear Schrödinger equation ͑DNLS͒ is derived with the use of the mean waveform method developed by Gurevich, Jeffrey, and Pelinovsky ͓Wave Motion 17, 287 ͑1993͔͒, which is the generalization of the reductive perturbation method for nonlinear waves propagating in random media. This equation differs from the standard DNLS equation by one additional term describing the interaction of nonlinear waves with random density fluctuations. As an example of the use of the modified DNLS equation, the quasi-adiabatic evolution of a one-parametric DNLS soliton propagating through a plasma with fluctuating density is studied.

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“…To transform the equations (3) and (7) into a wave equation with respect to the superfluid surface displacement, the reductive perturbation method by Tanuiti and Wei (1968) can be applied using the scaling transformation (9)…”

Section: Solitary Wavesmentioning

confidence: 99%

Solitons and their resonances on two-dimensional superfluid films

Sreekumar

Nandakumaran

1989

Pramana - J Phys

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Abstract. The dynamics of sa'turated two-dimensional superfluid 4He films is shown to be gO,verned by the Kadomtsev-Petviashvili equation with negative dispersion. It is established that the phenomena of soliton resonance could be observed in such films. Under the .lowest order nonjinearity, such resonance would happen only if two dimensional effects arc taken into ,account. The amplitude and velocity of the resonant soliton are obtained.

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Reductive Perturbation Method in Nonlinear Wave Propagation. I

Cited by 521 publications

References 2 publications

The effect of thermal expansion on nonlinear first and second sound in the whole temperature region of He II

The effect of thermal expansion on nonlinear first and second sound in the whole temperature region of He II

Propagation of solitons of the Derivative Nonlinear Schrödinger equation in a plasma with fluctuating density

Solitons and their resonances on two-dimensional superfluid films

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