Time-dependent defects described by Bäcklund transformations preserve integrability for NLS, KdV, and mKdV, and the moving-defect KdV system admits peaked (peakon) solutions.
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Time-dependent defects in integrable soliton equations
Time-dependent defects described by Bäcklund transformations preserve integrability for NLS, KdV, and mKdV, and the moving-defect KdV system admits peaked (peakon) solutions.