Orbital stability of solitary waves of the long wave-short wave resonance equations

Guo, Boling; Lin, Chen

doi:10.1002/(sici)1099-1476(19980710)21:10<883::aid-mma974>3.0.co;2-b

Cited by 22 publications

(3 citation statements)

References 15 publications

(20 reference statements)

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“…Corcho and Linares [19] considered the Cauchy problem of iq t + q xx = αqr + β|q| 2 q, r t + r xxx + 1 2 (r 2 ) x = γ(|q| 2 ) x , (α, β, γ ∈ R), (6) and obtained the local well-posedness. Guo and Chen [20] studied the orbital stability of solitary waves of the long-wave-short-wave resonance equations iq t + q xx = rq + α|q| 2 q, r t = (|q| 2 ) x , (α ∈ R), (7) from which they extended the abstract stability theory and used the detailed spectral analysis to obtain the stability of the solitary waves.…”

Section: Introductionmentioning

confidence: 99%

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

Geng

2019

Mathematics

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A vector modified Yajima–Oikawa long-wave–short-wave equation is proposed using the zero-curvature presentation. On the basis of the Riccati equations associated with the Lax pair, a method is developed to construct multi-fold classical and generalized Darboux transformations for the vector modified Yajima–Oikawa long-wave–short-wave equation. As applications of the multi-fold classical Darboux transformations and generalized Darboux transformations, various exact solutions for the vector modified long-wave–short-wave equation are obtained, including soliton, breather, and rogue wave solutions.

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Section: Introductionmentioning

confidence: 99%

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

Geng

2019

Mathematics

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“…Equations (1.4)-(1.5) have been extensively studied. For instance, the well-posedness of the Cauchy problem was investigated in [4,17]; the orbital stability of solitary waves was investigated in [13]; the existence of global attractors and random attractors was proved in [18,19]. The purpose of this article is to investigate the probability of solutions to the lattice long-waveshort-wave resonance equations (1.1)-(1.2) in weighted space.…”

Section: Introductionmentioning

confidence: 99%

Statistical solutions and Kolmogorov entropy for the lattice long-wave–short-wave resonance equations in weighted space

Zou,

Zhao,

Caraballo

2023

Communications in Nonlinear Science and Numerical Simulation

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“…Guo [3,4] proved the existence of global solutions for long-short wave equations and generalized long-short wave equations. The existence of global attractor was studied in [5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Existence of Random Attractor for Stochastic Fractional Long-Short Wave Equations with Periodic Boundary Condition

Liu¹,

Xin²

2017

Discrete Dynamics in Nature and Society

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We consider the asymptotic behaviors of stochastic fractional long-short equations driven by a random force. Under a priori estimates in the sense of expectation, using Galerkin approximation by the stopping time and the Borel-Cantelli lemma, we prove the existence and uniqueness of solutions. Then a global random attractor and the existence of a stationary measure are obtained via the Birkhoff ergodic theorem and the Chebyshev inequality.

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Orbital stability of solitary waves of the long wave-short wave resonance equations

Cited by 22 publications

References 15 publications

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

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

Statistical solutions and Kolmogorov entropy for the lattice long-wave–short-wave resonance equations in weighted space

Existence of Random Attractor for Stochastic Fractional Long-Short Wave Equations with Periodic Boundary Condition

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