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LONG-TIME ASYMPTOTICS OF THE KDV EQUATION WITH DELTA FUNCTION INITIAL PROFILES
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DOI：10.3934/cpaa.2026055.png)
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Abstract
En 中文
. This work investigates the long-time asymptotic behaviors of the solution to the KdV equation with delta function initial profiles in different regions, employing the Riemann-Hilbert formulation and Deift-Zhou nonlinear steepest descent method. Moreover, the general delta function initial profile with L-spikes is also studied, and it is proved that one to L solitons will be generated in the soliton region, which depends on the sizes of the distance and height of the spikes. The threshold for the number of solitons is exactly given by the zeros of the Chebyshev polynomials.
Keywords:
Riemann-Hilbert problem
Lax pair
KdV equation
delta function
soliton region
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0.9
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88
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