Darboux transformation and novel solutions for the long wave-short wave model

Huang, Xin; Guo, Boling; Ling, Liming

doi:10.1080/14029251.2013.868265

Cited by 9 publications

(3 citation statements)

References 18 publications

(28 reference statements)

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“…The complete integrability of the LWSW model ( 1)-( 2) was tested by Painlevé analysis [42]. Ling et al constructed its Darboux transformation and found a closed multi-soliton solution formula [43,44]. A class of cusp solution for the LWSW model ( 1)-( 2) was derived by using the dressing method [45].…”

Section: High-order Rational Solution In the Determinant Formmentioning

confidence: 99%

High-order rogue waves of a long-wave–short-wave model of Newell type

Chen

Feng

et al. 2019

Phys. Rev. E

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The long wave-short wave model describes the interaction between the long wave and the short wave. Exact higher-order rational solution expressed by determinants is calculated via the Hirota's bilinear method and the KP hierarchy reduction. It is found that the fundamental rogue wave for the short wave can be classified into three different patterns: bright, intermediate and dark ones, whereas the rogue wave for the long wave is always bright type. The higher-order rogue waves correspond to the superposition of fundamental rogue waves. The modulation instability analysis show that the condition of the baseband modulation instability where an unstable continuous-wave background corresponds to perturbations with infinitesimally small frequencies, coincides with the condition for the existence of rogue-wave solutions.

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Section: High-order Rational Solution In the Determinant Formmentioning

confidence: 99%

High-order rogue waves of a long-wave–short-wave model of Newell type

Chen

Feng

et al. 2019

Phys. Rev. E

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“…For the singular RH problems, we can transform it into regular RH problems by using the dressing method [33]. In the abstract, we can solve the solution of singular RH problems accurately by the Plemelj formula and dressing method [34]- [38]. However, when the reflection coefficient has multiple higher-order poles [39], the ansatz using the dressing matrix may become complex.…”

Section: The Riemann-hilbert Problemmentioning

confidence: 99%

The bound-state soliton solutions of a higher-order nonlinear Schrödinger equation for inhomogeneous Heisenberg ferromagnetic system

Mao

Tian

et al. 2021

Nonlinear Dyn

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By studying an appropriate Riemann-Hilbert (RH) problem, the inverse scattering of a higher-order nonlinear Schrödinger equation for inhomogeneous Heisenberg ferromagnetic system with zero boundary condition is calculated. The RH problem of reflection coefficient with multiple high-order poles is obtained. Meanwhile, the calculation formulas of bound state (BS) solitons and multiple BS solitons corresponding to one high-order pole and multiple high-order poles are also calculated respectively. Finally, the corresponding soliton solution model is calculated according to the corresponding formula. Simultaneously, we also obtain the interaction between BS soliton and multiple BS solitons, and between multiple BS solitons and multiple BS solitons. Keywords A higher-order nonlinear Schrödinger equation • Heisenberg ferromagnetism system • Riemann-Hilbert problem • Initial value problem • Multiple higher-order poles • Bound-state soliton solution.

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“…The singular RHP can be transformed to a regular one by dressing method [33]. Theoretically, based on the dressing method and Plemelj formula, the solution of singular RHP can be solved exactly [34][35][36][37][38][39]. However, the ansatz for dressing matrix may be very complicated when the reflection coefficient has multiple higher-order poles [40].…”

Section: The Riemann-hilbert Problemmentioning

confidence: 99%

The bound-state soliton solutions of the complex modified KdV equation

Zhang

Tao

2020

Inverse Problems

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The inverse scattering method is performed to the complex modified Korteweg-de Vries equation with zero boundary condition by developing an appropriate Riemann-Hilbert problem (RHP). We solve the RHP when reflection coefficient has multiple higher-order poles, and display the formulae of bound-state (BS) solitons and multiple BS solitons which correspond to one higher-order pole and multiple higher-order poles, respectively. The patterns of the BS solitons are shown and the interactions between solitons and BS solitons are considered.

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Darboux transformation and novel solutions for the long wave-short wave model

Cited by 9 publications

References 18 publications

High-order rogue waves of a long-wave–short-wave model of Newell type

High-order rogue waves of a long-wave–short-wave model of Newell type

The bound-state soliton solutions of a higher-order nonlinear Schrödinger equation for inhomogeneous Heisenberg ferromagnetic system

The bound-state soliton solutions of the complex modified KdV equation

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