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- W1976521070 abstract "Abstract We analyze the derivative nonlinear Schrodinger equation i q t + q x x = i ( | q | 2 q ) x on the half-line using the Fokas method. Assuming that the solution q ( x , t ) exists, we show that it can be represented in terms of the solution of a matrix Riemann–Hilbert problem formulated in the plane of the complex spectral parameter ζ . The jump matrix has explicit x , t dependence and is given in terms of the spectral functions a ( ζ ) , b ( ζ ) (obtained from the initial data q 0 ( x ) = q ( x , 0 ) ) as well as A ( ζ ) , B ( ζ ) (obtained from the boundary values g 0 ( t ) = q ( 0 , t ) and g 1 ( t ) = q x ( 0 , t ) ). The spectral functions are not independent, but related by a compatibility condition, the so-called global relation. Given initial and boundary values { q 0 ( x ) , g 0 ( t ) , g 1 ( t ) } such that there exist spectral functions satisfying the global relation, we show that the function q ( x , t ) defined by the above Riemann–Hilbert problem exists globally and solves the derivative nonlinear Schrodinger equation with the prescribed initial and boundary values." @default.
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- W1976521070 date "2008-12-01" @default.
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- W1976521070 title "The derivative nonlinear Schrödinger equation on the half-line" @default.
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- W1976521070 doi "https://doi.org/10.1016/j.physd.2008.07.005" @default.
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