Asymptotics in the critical case for Whitham type equations

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• 作者：Nakao Hayashi ; Elena I. Kaikina ; Pavel I. Naumkin
• 关键词：Dispersive system ; Solitary wave ; Stability
• 刊名：Nonlinear Analysis
• 出版年：2007
• 出版时间：15 November 2007
• 年：2007
• 卷：67
• 期：10
• 页码：2914-2933
• 全文大小：366 K

文摘

Consider the Cauchy problem for nonlinear dissipative evolution equations

where is the linear pseudodifferential operator and the nonlinearity is a quadratic pseudodifferential operator

is direct Fourier transformation. Let the initial data , , are sufficiently small and have a non-zero total mass , here is the weighted Sobolev space. Then we prove that the main term of the large time asymptotics of solutions in the critical case is given by the self-similar solution defined uniquely by the total mass M of the initial data.