New peaked solitary wave solutions of the generalized Camassa–Holm equation

Li, Tian; Song, Xiaoqiu

doi:10.1016/s0960-0779(03)00192-9

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Introduction4

Lemma 7 If U and F Are Functions In H Q+11

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Cited by 93 publications

(36 citation statements)

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“…Applying the inequality (17) with q + 1 = s and the bounded property of solution u (see (39) and (58)), we have…”

Section: Lemma 7 If U and F Are Functions In H Q+1mentioning

confidence: 99%

See 1 more Smart Citation

The local well-posedness and existence of weak solutions for a generalized Camassa–Holm equation

Lai

2010

Journal of Differential Equations

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A generalization of the Camassa-Holm equation, a model for shallow water waves, is investigated. Using the pseudoparabolic regularization technique, its local well-posedness in Sobolev space H s (R) with s > 3 2 is established via a limiting procedure. In addition, a sufficient condition for the existence of weak solutions of the equation in lower order Sobolev space H s with 1 < s 3 2 is developed.

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“…Applying the inequality (17) with q + 1 = s and the bounded property of solution u (see (39) and (58)), we have…”

Section: Lemma 7 If U and F Are Functions In H Q+1mentioning

confidence: 99%

“…When n = 3, two types of exact traveling wave solutions to Eq. (2) were acquired in [39]. For any exponent n of the nonlinearity, the integral expressions of traveling wave solutions for Eq.…”

Section: Introductionmentioning

confidence: 99%

The local well-posedness and existence of weak solutions for a generalized Camassa–Holm equation

Lai

2010

Journal of Differential Equations

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“…It is interesting to note that Ma, Yu and Ge [15] used a generalized auxiliary equation method to study the mDP equation differently. Some researchers studied the bifurcations and peakons of the mCH equations [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

New travelling wave solutions to modified CH and DP equations

Liang

Jeffrey

2009

Computer Physics Communications

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“…Recently, there is a growing research in the modified form of the Camassa-Holm equation. For example, Tian and Song [14] gave some explicit expressions of peakon waves for Eq.(1.1). Khuri [4] obtained some discontinuous solitary wave solutions for Eq.(1.1).…”

Section: Introductionmentioning

confidence: 99%