On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation

Geng, Xianguo; Li, Ruomeng

doi:10.3390/math7100958

Cited by 8 publications

(13 citation statements)

References 59 publications

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“…• The higher-order RW solutions given in Refs. [82][83][84] comprise N (N +1)/2 fundamental RWs, which correspond to the family of RW solutions in Theorem 2 of the present paper. The general higher-order RW solutions in Theorems 3 and 4 are new RW solutions to the 2-LSRI model (5), which have not been reported before, to the best of our knowledge.…”

Section: Conclusion and Discussionmentioning

confidence: 66%

General higher—order breathers and rogue waves in the two‐component long‐wave–short‐wave resonance interaction model

et al. 2022

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General higher-order breather and rogue wave (RW) solutions to the two-component long wave-short wave resonance interaction (2-LSRI) model are derived via the bilinear Kadomtsev-Petviashvili hierarchy reduction method and are given in terms of determinants. Under particular parametric conditions, the breather solutions can reduce to homoclinic orbits, or a mixture of breathers and homoclinic orbits. There are three families of RW solutions, which correspond to a simple root, two simple roots, and a double root of an algebraic equation related to the dimension reduction procedure. The first family of RW solutions consists of N (N +1) 2 bounded fundamental RWs, the second family is composed of N1(N1+1) 2 bounded fundamental RWs coexisting with another N2(N2+1) 2 fundamental RWs of different bounded state (N, N 1 , N 2 being positive integers), while the third one have [ N 2 1 + N 2 2 − N 1 ( N 2 − 1)] fundamental bounded RWs ( N 1 , N 2 being non-negative integers). The second family can be regarded as the superpositions of the first family, while the third family can be the degenerate case of the first family under particular parameter choices. These diverse RW patterns are illustrated graphically.

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Section: Conclusion and Discussionmentioning

confidence: 66%

General higher—order breathers and rogue waves in the two‐component long‐wave–short‐wave resonance interaction model

et al. 2022

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“…has been derived in [11] from a 3 × 3 matrix Lax pair, which is however different from the Lax pair investigated in the present paper (see Sections 2 and 3), and is not discussed here.…”

Section: Integrable Models Of Long Wave-short Wave Resonant Interactionmentioning

confidence: 91%

“…Other LS wave integrable equations may be sorted out via transformations of the wave fields. Indeed, the two integrable LS equations ( 5) and ( 4) may be given an equivalent, even simpler, form by performing the gauge transformation [5,11]…”

Section: Integrable Models Of Long Wave-short Wave Resonant Interactionmentioning

confidence: 99%

A new integrable model of long wave-short wave interaction and linear stability spectra

Caso-Huerta,

Degasperis,

Lombardo

et al. 2021

Preprint

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We consider the propagation of short waves which generate waves of much longer (infinite) wave-length. Model equations of such long wave-short wave resonant interaction, including integrable ones, are well-known and have received much attention because of their appearance in various physical contexts, particularly fluid dynamics and plasma physics. Here we introduce a new long wave-short wave integrable model which generalises those first proposed by Yajima-Oikawa and by Newell. By means of its associated Lax pair, we carry out the linear stability analysis of its continuous wave solutions by introducing the stability spectrum as an algebraic curve in the complex plane. This is done starting from the construction of the eigenfunctions of the linearised long wave-short wave model equations. The geometrical features of this spectrum are related to the stability/instability properties of the solution under scrutiny. Stability spectra for the plane wave solutions are fully classified in the parameter space together with types of modulational instabilities.

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“…Thus, these LS equations have been generalized to multicomponent short waves, either in vector form, as in [9], or in matrix form as in [10] requiring a higher rank matrix Lax pair. A third LS wave scalar equation, which reads iSt+Sxx+ifalse(LSfalse)x−2|Sfalse|2S=0,1emLt=2false(|Sfalse|2false)x, has been derived in [11] from a 3×3 matrix Lax pair, which is however different from the Lax pair investigated in the present paper (see §§2 and 3), and is not discussed here.…”

Section: Integrable Models Of Long Wave–short Wave Resonant Interactionmentioning

confidence: 92%

“…Other LS integrable equations may be sorted out via transformations of the wave fields. Indeed, the two integrable LS equations (1.5) and (1.4) may be given an equivalent, even simpler, form by performing the gauge transformation [5,11] Sfalse(x,tfalse)=eiϕfalse(x,tfalse)Sfalse^false(x,tfalse),1emLfalse(x,tfalse)=Lfalse^false(x,tfalse),1emϕx=μL,1emϕt=2μfalse(|Sfalse|2false). This transformation, which introduces the extra real parameter μ, originates from the conservative form of the evolution equation for the long wave amplitude L, in both the systems (1.5) and (1.4). Thus gauge transforming the YON system (1.5) yields the three parameter family of LS resonance equations itrueS^t+trueS^xx+2iμL^trueS^x+{(α+μ)[itrueL^x+(α−μ)trueL^2…”

Section: Integrable Models Of Long Wave–short Wave Resonant Interactionmentioning

confidence: 99%

A new integrable model of long wave–short wave interaction and linear stability spectra

et al. 2021

View full text Add to dashboard Cite

We consider the propagation of short waves which generate waves of much longer (infinite) wavelength. Model equations of such long wave–short wave (LS) resonant interaction, including integrable ones, are well known and have received much attention because of their appearance in various physical contexts, particularly fluid dynamics and plasma physics. Here we introduce a new LS integrable model which generalizes those first proposed by Yajima and Oikawa and by Newell. By means of its associated Lax pair, we carry out the linear stability analysis of its continuous wave solutions by introducing the stability spectrum as an algebraic curve in the complex plane. This is done starting from the construction of the eigenfunctions of the linearized LS model equations. The geometrical features of this spectrum are related to the stability/instability properties of the solution under scrutiny. Stability spectra for the plane wave solutions are fully classified in the parameter space together with types of modulational instabilities.

show abstract

On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation

Cited by 8 publications

References 59 publications

General higher—order breathers and rogue waves in the two‐component long‐wave–short‐wave resonance interaction model

General higher—order breathers and rogue waves in the two‐component long‐wave–short‐wave resonance interaction model

A new integrable model of long wave-short wave interaction and linear stability spectra

A new integrable model of long wave–short wave interaction and linear stability spectra

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