Nonlinear Schrodinger-Airy system

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The nonlinear Schrodinger-Airy system

on R is a combination of the cubic NLS equation, the derivative cubic NLS equation, complex mKdV, and a cubic nonlinear Airy equation. This equation is a general model for propagation of pulses in an optical fiber Kod1985, HasKod1987.

When , scaling is .When , scaling is -1/2.

LWP is known when . St1997d

For this is in Lau1997, Lau2001

The result is also known when is a time-dependent function Cv2002, CvLi2003

For and or non-zero, the solution map is not .

When LWP is known for Cv2004

For the solution map is not CvLi-p