New travelling wave solutions to modified CH and DP equations

Liang, Shuxiu; Jeffrey, David J.

doi:10.1016/j.cpc.2009.02.015

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New Traveling Wave Solutions For Mch Equation1

Introduction1

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2022

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Cited by 3 publications

(2 citation statements)

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“…A rational solution and more exact traveling wave solutions of Eq. ( 31) were also constructed by Liang and Jeffrey in [42].…”

Section: New Traveling Wave Solutions For Mch Equationmentioning

confidence: 99%

On classification of the solutions for general elliptic equation

2018

Preprint

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The Bäcklund transformations and the superposition formulas for two subequations of the general elliptic equation are constructed from the Riccati equation by using an indirect mapping method. The thirty-six previously known solutions of the general elliptic equation are proved to be equivalent to the another ten solutions. The classification of solutions for the general elliptic equation is obtained based on the equivalence relations. The general elliptic equation expansion method with new classified solutions are used to obtain abundant new exact traveling wave solutions of a modified Camassa-Holm equation.

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“…A rational solution and more exact traveling wave solutions of Eq. ( 31) were also constructed by Liang and Jeffrey in [42].…”

Section: New Traveling Wave Solutions For Mch Equationmentioning

confidence: 99%

On classification of the solutions for general elliptic equation

2018

Preprint

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“…For more results to Equation (1.3), please refer to Refs. [10,15,18]. Recently, Wu and Guo [21] considered the Cauchy problem of Equation (1.3), and they showed that the local wellposedness and wave breaking phenomena of solutions.…”

Section: Introductionmentioning

confidence: 99%

Global solutions for the modified Camassa–Holm equation

Zhou

2022

Z Angew Math Mech

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This paper is concerned with the global solutions for the modified Camassa-Holm equation. We first obtain the global existence and uniqueness of strong solutions for the initial datum 𝑢 0 (𝑥) ∈ 𝐻 𝑠 (ℝ) with 𝑠 > 3∕2, and then give some norm estimates of strong solutions and its momentum density. Finally, by using the compensated compactness method and regularization technique, we establish the global existence and uniqueness of weak solutions for the initial datum 𝑢 0 (𝑥) ∈ 𝐻 1 (ℝ).

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A note on exact travelling wave solutions for the modified Camassa–Holm and Degasperis–Procesi equations

Deng

2011

Applied Mathematics and Computation

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New travelling wave solutions to modified CH and DP equations

Cited by 3 publications

References 22 publications

On classification of the solutions for general elliptic equation

On classification of the solutions for general elliptic equation

Global solutions for the modified Camassa–Holm equation

A note on exact travelling wave solutions for the modified Camassa–Holm and Degasperis–Procesi equations

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