Travelling wave solutions in a class of generalized Korteweg-de Vries equation

Jianwei Shen; Wei Xu

doi:10.1016/j.chaos.2006.04.027

Travelling wave solutions in a class of generalized Korteweg-de Vries equation

Jianwei Shen, Wei Xu

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper, we consider a new generalization of KdV equation u_t = u_xu^l-2 + α[2u_xxxu^p + 4pu^p-1u_xu_xx + p(p - 1)u^{p- 2}(u_x)³] and investigate its bifurcation of travelling wave solutions. From the above analysis, we know that there exists compacton and cusp waves in the system. We explain the reason that these non-smooth travelling wave solution arise by using the bifurcation theory.

Original language	English
Pages (from-to)	1299-1306
Number of pages	8
Journal	Chaos, Solitons and Fractals
Volume	34
Issue number	4
DOIs	https://doi.org/10.1016/j.chaos.2006.04.027
State	Published - Nov 2007

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title = "Travelling wave solutions in a class of generalized Korteweg-de Vries equation",

abstract = "In this paper, we consider a new generalization of KdV equation ut = uxul-2 + α[2uxxxup + 4pup-1uxuxx + p(p - 1)up- 2(ux)3] and investigate its bifurcation of travelling wave solutions. From the above analysis, we know that there exists compacton and cusp waves in the system. We explain the reason that these non-smooth travelling wave solution arise by using the bifurcation theory.",

author = "Jianwei Shen and Wei Xu",

year = "2007",

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AU - Xu, Wei

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N2 - In this paper, we consider a new generalization of KdV equation ut = uxul-2 + α[2uxxxup + 4pup-1uxuxx + p(p - 1)up- 2(ux)3] and investigate its bifurcation of travelling wave solutions. From the above analysis, we know that there exists compacton and cusp waves in the system. We explain the reason that these non-smooth travelling wave solution arise by using the bifurcation theory.

AB - In this paper, we consider a new generalization of KdV equation ut = uxul-2 + α[2uxxxup + 4pup-1uxuxx + p(p - 1)up- 2(ux)3] and investigate its bifurcation of travelling wave solutions. From the above analysis, we know that there exists compacton and cusp waves in the system. We explain the reason that these non-smooth travelling wave solution arise by using the bifurcation theory.

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M3 - 文章

AN - SCOPUS:34247141903

SN - 0960-0779

VL - 34

SP - 1299

EP - 1306

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

IS - 4

ER -

Travelling wave solutions in a class of generalized Korteweg-de Vries equation

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