关于dKP方程的解：非线性Riemann Hilbert问题，长时间行为，隐式解和波破碎
On the solutions of the dKP equation: nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking
摘要：
利用无色散Kadomtsev Petviashvili方程的非线性Riemann-Hilbert问题，i）构造了其Cauchy问题解的长时间行为; ii）刻画了一类隐式解的特征; iii）阐明了在有限时间和长时间区域内，引起局部解梯度突变的谱机制，以及相应的在破裂附近的普遍行为.
英文摘要：
We make use of the nonlinear Riemann Hilbert problem of the dispersionless Kadomtsev Petviashvili equation, i) to construct the longtime behaviour of the solutions of its Cauchy problem; ii) to characterize a class of implicit solutions; iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking.
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