A study on resonant collision in the two-dimensional multi-component long-wave–short-wave resonance system

Rao, J. V.; Kanna, T.; He, Jing

doi:10.1098/rspa.2021.0777

Cited by 10 publications

(7 citation statements)

References 61 publications

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“…(2) 0 ) are two simple roots of the algebraic equation (86), then the tau functions are expressed by the following 2 × 2 block determinants:…”

Section: Derivation Of Higher-order Breather and Rw Solutionsmentioning

confidence: 99%

“…for a double root of Equation (86), where (𝑝) is given by Equation (103). Here, â𝑟 , â𝑟,𝛼 are arbitrary complex parameters.…”

Section: 3mentioning

confidence: 99%

“…85 However, higher order breather and homoclinic-orbit solutions have not been reported, as yet, for the 2-LSRI model (5), to the best of our knowledge. Very recently, we constructed general higher order breather solutions for the multicomponent two-dimensional LSRI model in terms of determinants via the bilinear KP-hierarchy reduction method, 86 which can also be applied to derive the higher order breather and homoclinic-orbit solutions of the 2-LSRI model (5) in the form of determinants.…”

Section: Introductionmentioning

confidence: 99%

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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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“…(2) 0 ) are two simple roots of the algebraic equation (86), then the tau functions are expressed by the following 2 × 2 block determinants:…”

Section: Derivation Of Higher-order Breather and Rw Solutionsmentioning

confidence: 99%

“…for a double root of Equation (86), where (𝑝) is given by Equation (103). Here, â𝑟 , â𝑟,𝛼 are arbitrary complex parameters.…”

Section: 3mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…The resonant interaction between the breathers and line solitons in Mel'nikov equation, KP-I equations and (2 + 1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation as well as the resonant interaction between breathers in two-dimensional multi-component longwave-short-wave resonant interaction system were studied in Refs. [38][39][40][41]. In this paper, we investigate the resonant interaction among the line solitons, breathers and lumps for the (2 + 1)-dimensional elliptic Toda equation.…”

Section: Introductionmentioning

confidence: 99%

Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the (2+1)-dimensional elliptic Toda equation

2023

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The (2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semi-discrete Kadomtsev-Petviashvili I equation. This paper focuses on investigating the resonant interactions between two breathers, a breather/lump and line solitons as well as lump molecules for the (2+1)-dimensional elliptic Toda equation. Based on the N-soliton solution, we obtain the hybrid solutions consisting of line solitons, breathers and lumps. Through the asymptotic analysis of these hybrid solutions, we derive the phase shifts of the breather, lump and line solitons before and after the interaction between a breather/lump and line solitons. By making the phase shifts infinite, we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons. Through the asymptotic analysis of these resonant solutions, we demonstrate the resonant interactions exhibit the fusion, fission, time-localized breather and rogue lump phenomena. Utilizing the velocity resonance method, we obtain lump-soliton, lump-breather, lump-soliton-breather and lump-breather-breather molecules. The above works have not been reported in the (2+1)-dimensional discrete nonlinear wave equations.

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“…[ 15–21 ] Over the past several years, many authors have concentrated on investigating the interaction properties, dynamic behaviors, and mechanisms of these localized waves in coupled systems. [ 22–30 ]…”

Section: Introductionmentioning

confidence: 99%

Interactions of Localized Wave Structures on Periodic Backgrounds for the Coupled Lakshmanan–Porsezian–Daniel Equations in Birefringent Optical Fibers

Guo

2022

Annalen der Physik

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Nonlinear waves on periodic backgrounds play an important role in physical systems. In this study, nonlinear waves that include solitons, breathers, rogue waves, and semi-rational solutions on periodic backgrounds for the coupled Lakshmanan-Porsezian-Daniel equations are investigated. Moreover, the interactions between different types of nonlinear waves are examined and their dynamic behaviors are studied. In particular, it is observed that bright-dark rogue waves interact with bright-dark breathers or solitons on periodic backgrounds, four-petaled breathers interact with two eye-shaped breathers on periodic backgrounds, and a four-petal rogue wave interplays with a rogue wave on periodic backgrounds. Furthermore, it is found that the value of the parameter 𝜸 3 affects the weak and strong interactions of these nonlinear waves. These results may be useful in the study of nonlinear wave dynamics in coupled nonlinear wave models.

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A study on resonant collision in the two-dimensional multi-component long-wave–short-wave resonance system

Cited by 10 publications

References 61 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

Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the (2+1)-dimensional elliptic Toda equation

Interactions of Localized Wave Structures on Periodic Backgrounds for the Coupled Lakshmanan–Porsezian–Daniel Equations in Birefringent Optical Fibers

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