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The Hirota τ-function and well-posedness of the KdV equation with an arbitrary step like initial profile decaying on the right half line
Korteweg-de Vries equation inverse scattering transform Schr ¨odinger operator
2010/12/28
We are concerned with the Cauchy problem for the KdV equation on the whole line with an initial profile V0 which is decaying sufficiently fast at +¥ and arbitrarily enough (i.e., no decay or patte...
Delta function singularity in the Reduction of Radial Schrodinger Equation
Laplace operator radial equation boundary condition singular potentials
2010/12/8
We obtain the extra delta-like singularity while reduction of the Laplace operator in spherical coordinates, elimination of which restricts the radial wave functions at the origin. This restriction ha...
What is the boundary condition for radial wave function of the Schrödinger equation ?
Schrodinger equation radial equation boundary condition
2010/12/15
The mathematical physics literatures as well as quantum mechanics textbooks on spherically symmetric potentials are enormous. Despite of these there is no unique point of view about the boundary behav...