Fifth-order evolution equations describing pseudospherical surfaces

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• 作者：V.P. Gomes Neto
• 关键词：Pseudospherical surface equations ; Fifth-order evolution equations
• 刊名：Journal of Differential Equations
• 出版年：2010
• 出版时间：1 December 2010
• 年：2010
• 卷：249
• 期：11
• 页码：2822-2865
• 全文大小：415 K

文摘

We consider differential equations which describe pseudospherical surfaces, with associated 1-forms , 1i3. We characterize all such equations of type u_t=u_xxxxx+G(u,u_x,…,u_xxxx) whose associated 1-forms satisfy f_p1=μ_pf₁₁+η_p, , 2p3, in addition to a generic technical assumption. We also classify all of these equations which are independent of any of the real parameters μ_p, η_p, obtaining as particular cases the fifth-order Korteweg–de Vries, the Sawada–Kotera and the Kaup–Kupershmidt equations. We determine huge classes of equations describing pseudospherical surfaces and their respective linear problems in which particular cases are obtained by merely specifying certain functions which depend on u and its derivatives with respect to x.