Existence and Uniqueness for Periodic Solutions of the Benjamin–Bona–Mahony Equation

Medeiros, L. A.; Menzala, G. Perla

doi:10.1137/0508062

Cited by 80 publications

(34 citation statements)

References 4 publications

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“…Existence and uniqueness results of this sort can be proved under a variety of hypotheses. Well-posedness of (1.2) is proved in [1], [3], [13], [14], [15], [18]. The following theorem, the proof of which is indicated in the Appendix, is similar, but not identical, to several appearing elsewhere [10], [18], [19].…”

mentioning

confidence: 99%

Superconvergence of a Finite Element Approximation to the Solution of a Sobolev Equation in a Single Space Variable

Arnold¹,

Douglas²,

Thomée³

1981

Mathematics of Computation

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confidence: 99%

Superconvergence of a Finite Element Approximation to the Solution of a Sobolev Equation in a Single Space Variable

Arnold¹,

Douglas²,

Thomée³

1981

Mathematics of Computation

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“…(1.1) can be regarded as a combination of Burgers equation and a simplified form of BBM equation proposed in [1,5]. In [10], Zhang rational fraction of exponential functions for (1.1) by using undetermined coefficients method.…”

Section: Introductionmentioning

confidence: 99%

Qualitative analysis and solutions of bounded traveling wave for B-BBM equation

Zhao

Zhang

2010

Acta Math. Appl. Sin. Engl. Ser.

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In this paper, we apply the theory of planar dynamical systems to carry out qualitative analysis for the dynamical system corresponding to B-BBM equation, and obtain global phase portraits under various parameter conditions. Then, the relations between the behaviors of bounded traveling wave solutions and the dissipation coefficient µ are investigated. We find that a bounded traveling wave solution appears as a kink profile solitary wave solution when µ is more than the critical value obtained in this paper, while a bounded traveling wave solution appears as a damped oscillatory solution when µ is less than it. Furthermore, we explain the solitary wave solutions obtained in previous literature, and point out their positions in global phase portraits. In the meantime, approximate damped oscillatory solutions are given by means of undetermined coefficients method. Finally, based on integral equations that reflect the relations between the approximate damped oscillatory solutions and the implicit exact damped oscillatory solutions, error estimates for the approximate solutions are presented.

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“…In paper [5] Recently, several authors have studied the existence and uniqueness of solutions for the generalized BBM equation (see [3,4,6,7]). In this paper, we consider a generalized BBM equation in the form…”

Section: Introductionmentioning

confidence: 99%

Existence of periodic traveling wave solutions for a class of generalized BBM equation

Huang

1997

Appl Math Mech

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Existence and Uniqueness for Periodic Solutions of the Benjamin–Bona–Mahony Equation

Cited by 80 publications

References 4 publications

Superconvergence of a Finite Element Approximation to the Solution of a Sobolev Equation in a Single Space Variable

Superconvergence of a Finite Element Approximation to the Solution of a Sobolev Equation in a Single Space Variable

Qualitative analysis and solutions of bounded traveling wave for B-BBM equation

Existence of periodic traveling wave solutions for a class of generalized BBM equation

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