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

Guo, Boling; Lin, Chen

doi:10.1016/s1007-5704(96)90009-x

Cited by 9 publications

(12 citation statements)

References 12 publications

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“…The existence of global attractor was studied in [6][7][8]. The orbital stability of solitary waves for this system has been studied in [9]. In [10], Guo investigated the asymptotic behavior of solutions for the long-short wave equations with zero order dissipation in 2 per × 1 per .…”

Section: Introductionmentioning

confidence: 99%

Weakly Compact Uniform Attractor for the Nonautonomous Long-Short Wave Equations

Cui

Xin

2013

Abstract and Applied Analysis

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Solutions and weakly compact uniform attractor for the nonautonomous long-short wave equations with translation compact forces were studied in a bounded domain. We first established the existence and the uniqueness of the solution to the system by using Galerkin method and then obtained the uniform absorbing set and the weakly compact uniform attractor of the problem by applying techniques of constructing skew product flow in the extended phase space.

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Section: Introductionmentioning

confidence: 99%

Weakly Compact Uniform Attractor for the Nonautonomous Long-Short Wave Equations

Cui

Xin

2013

Abstract and Applied Analysis

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“…The existence of global solutions for long-short wave equations and generalized long-short wave equations are obtained by Guo in [8] and [9], respectively. The orbital stability of solitary waves and the existence of a global attractor have been studied in [6,10,11,15,22]. It is well known that stochastic partial differential equations (SPDEs) play an important role in understanding the dynamics of many interesting phenomena.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Random attractor and stationary measure for stochastic long-short wave equations

Guo

2015

Communications in Mathematical Sciences

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Asymptotic behaviors of stochastic long-short equations driven by a random force, which is smooth enough in space and white noise in time, are mainly considered. The existence and uniqueness of solutions for stochastic long-short equations are obtained via Galerkin approximation by the stopping time and the Borel-Cantelli Lemma on the basis of a priori estimates in the sense of expectation. A global random attractor and the existence of a stationary measure are investigated by the Birkhoff ergodic theorem and the Chebyshev inequality.

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“…The system (1.1) is integrable for the choices of parameters K i = 1, i = 1, 2, 3, 4, 5 [17]. Another relative long wave-short wave model was derived by Benney in 1977 [2], which had been widely researched, such as [8,12,15,16,19]. However, there is few research about the model (1.1).…”

Section: Introductionmentioning

confidence: 99%

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

Huang¹,

Guo²,

Ling³

2021

JNMP

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

Cited by 9 publications

References 12 publications

Weakly Compact Uniform Attractor for the Nonautonomous Long-Short Wave Equations

Weakly Compact Uniform Attractor for the Nonautonomous Long-Short Wave Equations

Random attractor and stationary measure for stochastic long-short wave equations

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

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