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4 papers · 1 filter
Long-Time Dynamics of KdV Solitary Waves over a Variable Bottom
S. I. Dejak, I. M. Sigal
We study the variable bottom generalized Korteweg-de Vries (bKdV) equation dt u=-dx(dx^2 u+f(u)-b(t,x)u), where f is a nonlinearity and b is a small, bounded and slowly varying fun…
Integrable Systems and Rank One Conditions for Rectangular Matrices
Michael Gekhtman, Alex Kasman
We provide a determinantal formula for tau-functions of the KP hierarchy in terms of rectangular, constant matrices , and satisfying a rank one condition. This result is…
Holomorphic Sobolev spaces and the generalized Segal-Bargmann transform
Brian C. Hall, Wicharn Lewkeeratiyutkul
We consider the generalized Segal-Bargmann transform C_t for a compact group K, introduced in B. C. Hall, J. Funct. Anal. 122 (1994), 103-151. Let K_C denote the complexification o…
Solitary Wave Dynamics in an External Potential
J. Frohlich, S. Gustafson, B. L. G. Jonsson +1
We study the behavior of solitary-wave solutions of some generalized nonlinear Schrödinger equations with an external potential. The equations have the feature that in the absence…