Xifang Cao

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and Applied Analysis 3 is integrable; moreover, v also solves 1.9 . So 1.10 gives a transformation u → v, now called Bäcklund transformation, which takes one solution of 1.9 into another. For example, substituting the trivial solution u x, t ≡ 0 into 1.10 yields one-soliton solution: v x, t 4 arctan exp ( α − λx − 1 λ t ) , 1.11 where α is an arbitrary(More)
We consider some geometric aspects of regular eigenvalue problems of an arbitrary order. First, we clarify a natural geometric structure on the space of boundary conditions. This structure is the base for studying the dependence of eigenvalues on the boundary condition involved, and reveals new properties of these eigenvalues. Then, we solve the(More)
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