A method is given to construct globally analytic (in space and time) exact solutions to the focusing cubic nonlinear Schrodinger equation on the line. An explicit formula and its equivalents are presented to express such exact solutions in a compact form in terms of matrix exponentials. Such exact solutions can alternatively be written explicitly as algebraic combinations of exponential, trigonometric and polynomial functions of the spatial and temporal coordinates.
Exact solutions to the focusing nonlinear Schrödinger equation
DEMONTIS, FRANCESCO;VAN DER MEE, CORNELIS VICTOR MARIA
2007
Abstract
A method is given to construct globally analytic (in space and time) exact solutions to the focusing cubic nonlinear Schrodinger equation on the line. An explicit formula and its equivalents are presented to express such exact solutions in a compact form in terms of matrix exponentials. Such exact solutions can alternatively be written explicitly as algebraic combinations of exponential, trigonometric and polynomial functions of the spatial and temporal coordinates.
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