廣義 Rosenau-Kawahara 方程的有效譜方法

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摘要：針對廣義Rosenau-Kawahara方程提出了Legendre dual-Petrov-Galerkin 譜方法，并基于對 角化技巧，構(gòu)建了快速有效算法。在此基礎(chǔ)上研究了單個孤立波的傳播、守恒律及波的生成等物理現(xiàn)象。數(shù)值結(jié)果驗證了所提算法的有效性。

關(guān)鍵詞：Legendre dual-Petrov-Galerkin譜方法；廣義Rosenau-Kawahara方程；孤立波；守恒律

中圖分類號：O 241.82  文獻標(biāo)志碼：A

An efficient spectral method for the generalized Rosenau-Kawahara equation

WEN Xian， WANG Zhongqing

（College of Science， University of Shanghai for Science and Technology， Shanghai 200093， China）

Abstract： The Legendre dual-Petrov-Galerkin spectral method was proposed to the generalized Rosenau-Kawahara equation. A fast and efficient algorithm was constructed based on the diagonalization technique. The motion of single solitary wave solution， conservation laws and the phenomena of wave generation were also studied. Numerical results illustrate the effectiveness of the suggested approach.

Keywords： Legendre dual-Petrov-Galerkin spectral method; generalized Rosenau-Kawahara equation; solitary wave; conservation laws

1 問題提出及預(yù)備知識

非線性波的傳播是自然界中普遍存在的物理現(xiàn)象，對其進行數(shù)值研究具有十分重要的理論意義和應(yīng)用價值。（剩余6282字）