Asymptotic Analysis and Soliton Interactions of the Multi-Pole Solutions in the Hirota Equation

Li, Min; Zhang, Xuefeng; Xu, Tao; Li, Lingling

doi:10.7566/jpsj.89.054004

Cited by 37 publications

(24 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The complete integrability of the nonlinear system (1) is guaranteed by the presence of Lax pair. Once the Lax pair is known, one can efficiently exploit the Darboux transformation technique to construct various localized solutions [18][19][20][21] for the concerned equation. With the help of Darboux transformation method, we can construct a new solution ψ(x, t) = r (x, t) by providing a suitable seed solution ψ(x, t) = r (x, t).…”

Section: Lax Pair and Darboux Transformationmentioning

confidence: 99%

“…(1) reduces to the standard NLS equation. During the past two decades, several works have been devoted to construct and analyze the characteristics of localized solutions in the Hirota equation [16][17][18][19][20][21]. Multisolitons, breathers and rogue wave (RW) solutions have been constructed for the Hirota equation using different techniques, see for example Refs.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Rogue waves on the double-periodic background in Hirota equation

2021

View full text Add to dashboard Cite

We construct rogue wave solutions on the double-periodic background for the Hirota equation through onefold Darboux transformation formula. We consider two types of double-periodic solutions as seed solutions. We identify the squared eigenfunctions and eigenvalues that appear in the onefold Darboux transformation formula through an algebraic method with two eigenvalues. We then construct the desired solution in two steps. In the first step, we create double-periodic waves as the background. In the second step, we build rogue wave solution on the top of this double-periodic solution. We present the localized structures for two different values of the arbitrary parameter each one with two different sets of eigenvalues.

show abstract

Section: Lax Pair and Darboux Transformationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Rogue waves on the double-periodic background in Hirota equation

2021

View full text Add to dashboard Cite

show abstract

“…The higher-order pole soliton solutions can be derived from single pole-soliton solutions through limit procedures [29]. There are lot of researches were reported for the higher-order pole solitons in the local equations [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46], which focus on the long time asymptotic behaviours and interaction properties of the higher-order pole solitons. However, related results on higher-order pole solitons are scarce for the nonlocal equations.…”

Section: Introductionmentioning

confidence: 99%

Bright–dark solitons in the space-shifted nonlocal coupled nonlinear Schrödinger equation

Ren

Rao

2022

Nonlinear Dyn

View full text Add to dashboard Cite

Multiple bright-dark soliton solutions in terms of determinants for the space-shifted nonlocal coupled nonlinear Schrödinger (CNLS) equation are constructed by using the bilinear (Kadomtsev-Petviashvili) KP hierarchy reduction method. It is found that the bright-dark two-soliton only occur elastic collisions. Upon their amplitudes, the bright two solitons only admit one pattern whose amplitude are equal, and the dark two solitons have three different non-degenerated patterns and two different degenerated patterns. The bright-dark four-soliton is the superposition of the two-soliton pairs and can generated bound-state solitons. The multiple double-pole bright-dark soliton solutions are generated through the long wave limit of the obtained bright-dark soliton solutions, and their collision dynamics are also investigated.

show abstract

Section: Introductionmentioning

confidence: 99%

Bright--Dark Solitons in the Space-Shifted Nonlocal Coupled Nonlinear Schrodinger Equation

Ren

Rao

2021

Preprint

View full text Add to dashboard Cite

Multiple bright-dark soliton solutions in terms of determinants for the space-shifted nonlocal coupled nonlinear Schro¨dinger (CNLS) equation are constructed by using the bilinear (Kadomtsev-Petviashvili) KP hierarchy reduction method. It is found that the bright-dark two-soliton only occur elastic collisions. Upon their amplitudes, the bright two solitons only admit one pattern whose amplitude are equal, and the dark two solitons have three different non-degenerated patterns and two different degenerated patterns. The bright-dark four-soliton is the superposition of the two-soliton pairs and can generated bound-state solitons. The multiple double-pole bright-dark soliton solutions are generated through the long wave limit of the obtained bright-dark soliton solutions, and their collision dynamics are also investigated.PACS 02.30.Jr · 03.75.Lm · 04.20.Jb · 05.45.Yv

show abstract

Asymptotic Analysis and Soliton Interactions of the Multi-Pole Solutions in the Hirota Equation

Cited by 37 publications

References 42 publications

Rogue waves on the double-periodic background in Hirota equation

Rogue waves on the double-periodic background in Hirota equation

Bright–dark solitons in the space-shifted nonlocal coupled nonlinear Schrödinger equation

Bright--Dark Solitons in the Space-Shifted Nonlocal Coupled Nonlinear Schrodinger Equation

Contact Info

Product

Resources

About