Traveling Wave Solutions to Kadomtsev-Petviashvili Equation
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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.
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关键词:
- K-P方程 /
- 行波解 /
- 山路引理 /
- 存在性 /
- Sobolev紧嵌入定理
Abstract: The generalized K-P(Kadomtsev-Petviashvili) equation with two parameters was studied.The existence of traveling wave solution of this equation was proved under some exponentially increasing assumptions for nonlinear term by using the mountain pass theorem without Palais-Smale conditions and corresponding Sobolev compact embedding theorem. -
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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