Decomposition of Higher-Order Equations of Monge–Ampère Type

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• 作者：Ferapontov ; E. V.
• 关键词：B&auml ; cklund transformation ; decomposition ; Monge– ; Amp&egrave ; re equation
• 刊名：Letters in Mathematical Physics
• 出版年：2002
• 出版时间：2002
• 年：2002
• 卷：62
• 期：3
• 页码：193-198
• 全文大小：87 KB

文摘

It is demonstrated that the fourth-order PDE<math>\left| \matrix{f_{xxxx} & f_{xxxt} & f_{xxtt} \cr f_{xxxt}& f_{xxtt}& f_{xttt} \cr f_{xxtt}& f_{xttt}& f_{tttt}}\right| = 0math>decouples in a pair of identical second-order Monge–Amp&egrave;re equations,<math>u_{xx}u_{tt} - u_{xt}^2 = 0 \quad {\rm and} \quad {v}_{xx}{v}_{tt} - {v}_{xt}^2 = 0,math>by virtue of the B&auml;cklund-type relation<math>{\rm d}^4f={({\rm d}^2u)^2 \over u_{xx}}+ {({\rm d}^2{v})^2\over{v}_{xx}}.math>A higher order generalization of this decomposition ia also proposed.