• 偏导数 - 引用次数：3

  In this paper, we have applied the derivative-dependent functional variableseparation approach to discuss the following (1+1)-dimensional nonlinear evolution equation with mixed partial derivatives which has certain physical contexts:E≡E(t，x，u，u_1，u_2，…，U_m，U_(1t)，U_(2t)，…，U_(nt))=0．we have obtained some important results:(1) We have proposed the new theory of the derivative-dependent functionalvariable separation for the (1+1)-dimensional nonlinear evolution equationwith mixed partial derivatives;(2)We have constructed a relation between the derivative-dependent functionalvariable separation for the above class of equations and the functional variable separation for whose corresponding systems of PDEs;(3)As an application, we have obtained complete classification of the general nonlinear evolution equations u_(xt)=A(u,u_x)u_(xxx)+B(u,u_x) that admit DDFSSsand some DDFSSs.

  本论文运用导数相关泛函分离变量法，讨论了具有丰富物理背景的具混合偏导数的一般(1+1)维非线性演化方程E≡E(t，x，u，u_1，u_2，…，U_m，U_(1t)，U_(2t)，…，U_(nt))=0．得到了一些有意义的结果：(1)建立了该类型方程的导数相关泛函分离变量的一般理论；(2)建立了该类型方程的导数相关泛函分离变量与方程组的泛函分离变量的关系；(3)作为范例，给出了一般非线性演化方程u_(xt)=A(u，u_x)u_(xxx)+B(u，u_x)具有DDFSSs的完全归类和精确解。

  参考来源 - 一类（1+1）维非线性演化方程的导数相关泛函分离变量

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