An<i>N</i>-soliton solution to the DNLS equation based on revised inverse scattering transform

Zhou, Guoquan; Huang, Nian-Ning

doi:10.1088/1751-8113/40/45/008

Cited by 45 publications

(49 citation statements)

References 28 publications

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“…However, its applicability to studying the intermediate behaviour of solutions is restricted to the initial conditions for which the corresponding scattering problem can be solved analytically. To our knowledge, the only non-trivial exact solutions to the DNLS equation obtained so far are different kinds of the N-soliton solutions (see, e.,g., [48][49][50][51]). Since, at present, it is not clear if the scattering problem for the DNLS equation for the initial condition (17) can be solved analytically, the nonlinear evolution of this perturbation was studied numerically [43].…”

Section: Generation Of Large-amplitude Pulses Described By the Dnls Ementioning

confidence: 99%

Freak waves in laboratory and space plasmas

Рудерман

2010

Eur. Phys. J. Spec. Top.

137

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Abstract. Generation of large-amplitude short-lived wave groups from small-amplitude initial perturbations in plasmas is discussed. Two particular wave modes existing in plasmas are considered. The first one is the ion-sound wave. In a plasmas with negative ions it is described by the Gardner equation when the negative ion concentration is close to critical. The results of numerical solution of the Gardner equation with the modulationally unstable initial condition are presented. These results clearly show the possibility of generation of freak ionacoustic waves due to the modulational instability. The second wave mode is the Alfvén wave. When this wave propagates at a small angle with respect to the equilibrium magnetic field, and its wave length is comparable with the ion inertia length, it is described by the DNLS equation. Studying the evolution of an initial perturbation using the linearized DNLS equation shows that the generation of freak Alfvén waves is possible due to linear dispersive focusing. The numerical solution of the DNLS equation reveals that the nonlinear dispersive focusing can also produce freak Alfvén waves.

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Section: Generation Of Large-amplitude Pulses Described By the Dnls Ementioning

confidence: 99%

Freak waves in laboratory and space plasmas

Рудерман

2010

Eur. Phys. J. Spec. Top.

137

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“…The DNLS equation with both kinds of boundary conditions, vanishing and nonvanishing boundary conditions (VBC and NVBC for brevity, respectively), is of not only important physical application background, but also mathematical interest and significance. Some pioneering and fundamental work has been made and much progress has been attained by several scholars in solving the DNLS equation [10][11][12][13][14][15][16] . For the DNLS equation with VBC, one-soliton solution was attained by means of inverse scattering transform (IST) technique [11] .…”

Section: Introductionmentioning

confidence: 99%

“…For the DNLS equation with VBC, one-soliton solution was attained by means of inverse scattering transform (IST) technique [11] . The multi-soliton solution was also obtained by means of different approaches [14][15][16] . Especially, Ref.…”

Section: Introductionmentioning

confidence: 99%

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Soliton solution of the DNLS equation based on Hirota’s bilinear derivative transform

Zhou

2009

Wuhan Univ. J. Nat. Sci.

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Based on the method of Hirota's bilinear derivative transform, the derivative nonlinear Schrödinger equation with vanishing boundary condition has been directly solved. The oneand two-soliton solutions are given as two typical examples in the illustration of the general procedures and the concrete cut-off technique of the series-form solution, and the n-soliton solution is also attained by induction method. Our study shows their equivalence to the existing soliton solutions by a simple parameter transformation. The methodological importance of bilinear derivative transform in dealing with an integrable nonlinear equation has also been emphasized. The evolution of one and two-soliton solution with respect to time and space has been discussed in detail. The collision among the solitons has been manifested through an example of two-soliton case, revealing the elastic essence of the collision and the invariance of the soliton form and characteristics.

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The Derivative Nonlinear Schrödinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms and N-Double-Pole Solutions

Zhang

Yan

2020

J Nonlinear Sci

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AnN-soliton solution to the DNLS equation based on revised inverse scattering transform

Cited by 45 publications

References 28 publications

Freak waves in laboratory and space plasmas

Freak waves in laboratory and space plasmas

Soliton solution of the DNLS equation based on Hirota’s bilinear derivative transform

The Derivative Nonlinear Schrödinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms and N-Double-Pole Solutions

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