Soliton Solution for Discrete Hirota Equation<sup>*</sup>

Narita, Kazuaki

doi:10.1143/jpsj.59.3528

Cited by 54 publications

(36 citation statements)

References 4 publications

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“…The explicit expressions have been given earlier [19,20]. In particular, bright and rational solitons on a continuous wave background are also obtained for the case of dispersive and nonlinear terms of the same sign.…”

Section: Conclusion 5 1 Introductionmentioning

confidence: 93%

Periodic Waves of a Discrete Higher Order Nonlinear Schrödinger Equation

Conte

Chow

2006

Commun. Theor. Phys.

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The Hirota equation is a higher order extension of the nonlinear Schrödinger equation by incorporating third order dispersion and one form of self steepening effect. New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete periodic patterns reproduces the known result of the integrable Ablowitz-Ladik system.

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Section: Conclusion 5 1 Introductionmentioning

confidence: 93%

Periodic Waves of a Discrete Higher Order Nonlinear Schrödinger Equation

Conte

Chow

2006

Commun. Theor. Phys.

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“…Among them, we have the tanh-function method [41], the elliptic function approach [42], and the Hirota'sbilinearization method [29][30][31][32], to name just few. Here, the Hirota'sbilinearization method is used to investigate exact solitons solution of the PB model.…”

Section: Model and Mathematical Backgroundmentioning

confidence: 99%

“…Here, the Hirota'sbilinearization method is used to investigate exact solitons solution of the PB model. In so doing, the Hirota bilinear transformation F 1,n = g n /f n [29][30][31][32] is applied, where g n and f n are complex and real functions, respectively. Introducing the above transformation into equation 13 and decoupling the resultant equation lead to the bilinear equations (16) where the Hitota's bilinear operators D t and D n are defined by:…”

Section: Model and Mathematical Backgroundmentioning

confidence: 99%

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Formation and Interaction of Bright Solitons with Shape Changing in a DNA Model

Tabi¹

2014

J Phys Chem Biophys

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I explore the collision of localized structures that arise from a general initial solutions in the Peyrard-Bishop model. By means of the semi-discrete approximation, it is shown that the amplitudes of waves are described by the the discrete nonlinear Schrödinger equation. The corresponding soliton solutions of this equation are obtained through the Hirota's bilinearization method. These solutions include the one-as well as the two-soliton solutions. Particular attention is paid to the behaviors displayed by the two-soliton solution. Taking one of the soliton as a pump and the other as the bubble that describes the local opening of the two strands of DNA, I show that, the enhancement of the bubbles is due to energy transfer from the pump to the bubble within the collision process. It is also shown that the underlying solitons undergo fascinating shape changing (intensity redistribution) collision.

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“…23 Its bright and dark soliton solutions can be found using the Hirota bilinear method. 24,25 Discrete rogue waves in the form of rational solutions of IDHE (3) were given in Ref. 26.…”

Section: The Hirota Equation (He)mentioning

confidence: 99%

Solitons and dynamic properties of the coupled semidiscrete Hirota equation

Zhao

Zhu

2013

AIP Advances

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In this paper, we obtain the coupled bright-bright and the coupled dark-dark soliton solutions for an integrable coupled semidiscrete Hirota equation (ICDHE) using the bilinear method. These solutions have both singular and nonsingular behaviors depending upon the choice of the parameters. The distinguishing feature of the ICDHE is that the singular solution can possess some nonsingular characteristics in the discrete space at some time. The asymptotic behavior of these coupled bright-bright and the coupled dark-dark solitons is studied in order to explain their collision properties.

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Soliton Solution for Discrete Hirota Equation^*

Cited by 54 publications

References 4 publications

Periodic Waves of a Discrete Higher Order Nonlinear Schrödinger Equation

Periodic Waves of a Discrete Higher Order Nonlinear Schrödinger Equation

Formation and Interaction of Bright Solitons with Shape Changing in a DNA Model

Solitons and dynamic properties of the coupled semidiscrete Hirota equation

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Soliton Solution for Discrete Hirota Equation*

Cited by 54 publications

References 4 publications

Periodic Waves of a Discrete Higher Order Nonlinear Schrödinger Equation

Periodic Waves of a Discrete Higher Order Nonlinear Schrödinger Equation

Formation and Interaction of Bright Solitons with Shape Changing in a DNA Model

Solitons and dynamic properties of the coupled semidiscrete Hirota equation

Contact Info

Product

Resources

About

Soliton Solution for Discrete Hirota Equation^*