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Kadom tsev-Petviashvili型方程的行波解

胡越 杨晗

胡越, 杨晗. Kadom tsev-Petviashvili型方程的行波解[J]. 西南交通大学学报, 2006, 19(4): 537-540.
引用本文: 胡越, 杨晗. Kadom tsev-Petviashvili型方程的行波解[J]. 西南交通大学学报, 2006, 19(4): 537-540.
HU Yue, YANG Han. Traveling Wave Solutions to Kadomtsev-Petviashvili Equation[J]. Journal of Southwest Jiaotong University, 2006, 19(4): 537-540.
Citation: HU Yue, YANG Han. Traveling Wave Solutions to Kadomtsev-Petviashvili Equation[J]. Journal of Southwest Jiaotong University, 2006, 19(4): 537-540.

Kadom tsev-Petviashvili型方程的行波解

基金项目: 

国家自然科学基金资助项目(10301026)

详细信息
    作者简介:

    胡越(1960- ),男,副教授,研究方向为偏微分方程,E-mail:huu3y2@163.com

Traveling Wave Solutions to Kadomtsev-Petviashvili Equation

  • 摘要: 研究含有两个参数的K-P型方程.在非线性项满足一定指数增长条件下,利用泛函分析中的没有Palais-Sm ale条件的山路引理和相应的Sobolev紧嵌入定理,证明了该方程非平凡行波解的存在性.

     

  • KORTEWEG K J,DEVRIES G.On the change of form of long waves advancing in a rectangular channel and on a new type of long stationary waves[J].Philos.Mag.Ser.,1958,39(5):422-443.[2] KADOMDTSEY B B,PETVIASHVILI V I.On the stability of solitary wave in weakly dispersing media[J].Sovit.Phys.Doki.,1970,15:539-541.[3] LAEDKE W,SPATSCHEK K H.Nonlinear ion-acoustic waves in weak magnetic fields[J].J.Phys.Fluids,1982,25:985-989.[4] HIYAMOGGI B K S.Nonlinear ion-acoustic waves in weak magnetized plasma and Zakharov-Kuznetsov equation[J].J.Plasma Phys.,1989,41:83-88.[5] BOURGAIN J.On the Cauchy problem for the Kadomtesv-Petviashvili equation[J].Geometric and Functional Analysis,1993,3:315-341.[6] WILLEM M.On the generalized Kadomtsev-Petviashvili equation[J].Seminaire do Mathematique,1995,96:213-222.[7] SHIYAMOGGI B K.The painleve analysis of the Zakharov-Kuznetsov equation[J].Physica Scripa,1990,42:641-642.[8] AIZICOVICI S,WEN S L.Anti-perodic traveling wave solutions to a forced two-dimensional generalized Kdv equation[J].J.Math.and Anal.,1993,174:556-565.[9] BESOV O V,ILIN V P,NIKOLSKII S M.Integral representations of functions and imbeddings theorems[M].Vol Ⅰ.New York:Wiley,1978:50-89.[10] AMBROSETT I,RABINOWITZ P.Dual variational methods in critical point theory and applications[J].J.Funct.Analysis,1973:349-381.
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出版历程
  • 收稿日期:  2005-12-27
  • 刊出日期:  2006-08-25

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