Basing on the direct method developed by Clarkson and Kruskal, the nearly concentric Korteweg-de Vries （ncKdV） equation can be reduced to three types of （1＋1）-dimensional variable coefficients partial differentia...Basing on the direct method developed by Clarkson and Kruskal, the nearly concentric Korteweg-de Vries （ncKdV） equation can be reduced to three types of （1＋1）-dimensional variable coefficients partial differential equations （PDEs） and three types of variable coefficients ordinary differential equation. Furthermore, three types of （1＋1）-dimensional variable coefficients PDEs are all reduced to constant coefficients PDEs by some transformations.展开更多
Around the central theme of 'square root' of the Laplace operator it is shown that the classical Riesz potentials of the first and of the second kind allow for an explicit expression of so-called Hilbert-Dirac...Around the central theme of 'square root' of the Laplace operator it is shown that the classical Riesz potentials of the first and of the second kind allow for an explicit expression of so-called Hilbert-Dirac convolution operators involving natural and complex powers of the Dirac operator.展开更多
基金Supported by K.C. Wong Magna Fund in Ningbo University, NSF of China under Grant Nos. 10747141 and 10735030Zhejiang Provincial Natural Science Foundations of China under Grant No. 605408the Ningbo Natural Science Foundation under Grant Nos. 2007A610049 and 2006A610093
文摘Basing on the direct method developed by Clarkson and Kruskal, the nearly concentric Korteweg-de Vries （ncKdV） equation can be reduced to three types of （1＋1）-dimensional variable coefficients partial differential equations （PDEs） and three types of variable coefficients ordinary differential equation. Furthermore, three types of （1＋1）-dimensional variable coefficients PDEs are all reduced to constant coefficients PDEs by some transformations.
文摘Around the central theme of 'square root' of the Laplace operator it is shown that the classical Riesz potentials of the first and of the second kind allow for an explicit expression of so-called Hilbert-Dirac convolution operators involving natural and complex powers of the Dirac operator.
