We introduce a hierarchy of integrable partial differential equations in 2 + 1 dimensions arising from the commutation of 2 dimensional vector fields, and we construct the formal solution of the associated Cauchy problems using the Inverse Scattering Transform for one-parameter families of vector fields recently introduced in [1, 2]. Due to the ring property of the space of eigenfunctions, the ...

We present necessary and sufficient conditions on the Jost function for the corresponding Jacobi parameters an − 1 and bn to have a given degree of exponential decay.

We show that the parameters an, bn of a Jacobi matrix have a complete asymptotic series

We introduce generalized operator valued Jost solutions of first order ill-posed differential equations on Hilbert spaces. We then construct an infinite dimensional Evans function for abstract differential equations as a 2– modified Fredholm determinant of the operator obtained by adding the values at zero of the generalized operator valued Jost solutions. Next, we prove a formula that connects...

The one-dimensional Schrödinger equation is considered when the potential is real valued, integrable, and has a finite first moment. The small-energy asymptotics of the logarithmic spatial derivative of the Jost solutions are established. Some consequences of these asymptotics are presented such as the small-energy limits of the scattering coefficients and a simplified characterization of the s...

Elegant and mathematically rigorous methods of the quantum inverse theory are difficult to put into practice because there is always some lack of needful input information. In this situation, one may try to construct a reference potential, whose spectral characteristics would be in a reasonable agreement with the available data of the system’s properties. Since the reference potential is fixed,...

Areejit Samal, R.P. Sreejith, Jiao Gu, Shiping Liu, ∗ Emil Saucan, 5, † and Jürgen Jost 7, ‡ The Institute of Mathematical Sciences, Homi Bhabha National Institute, Chennai, India Jiangnan University, Wuxi, P.R. China School of Mathematical Sciences, University of Science and Technology of China, Hefei, P.R. China Department of Applied Mathematics, ORT Braude College, Karmiel, Israel Department...

We consider wave scattering in a forked-shaped waveguide which consists of two finite and one half-infinite intervals having one common vertex. We describe the spectrum of the direct scattering problem and introduce an analogue of the Jost function. In case of the potential which is identically equal to zero on the half-infinite interval, the problem is reduced to a problem of the Regge type. F...

Dies ist eine Internet-Sonderausgabe des Aufsatzes " The formation of comparatives in the history of Georgian I: The prehistory of the synthetic comparatives " von Jost Gippert (1996). Sie sollte nicht zitiert werden. Zitate sind der Originalausgabe in Enatmecnierebis Sak'itxebi (V =) 1/2000, 37-45 zu entnehmen. Attention! This is a special internet edition of the article " The formation of com...

Dies ist eine englischsprachige Internet-Sonderausgabe des Aufsatzes " St. Nino's Legend: Vestiges of its various sources " von Jost Gippert (1997). Sie sollte nicht zitiert werden. Zitate sind der georgischen Originalausgabe " ~m. ninos legenda: gansXvavebul ~qarota kvali " in Enatmecnierebis Sak'itxebi 1-2/2006, 104-122 zu entnehmen. Attention! This is a special English internet edition of th...