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This paper is a continuation of arXiv:17.01.02867. We give here rigorous solution of the parametrix problem for Toda rarefaction problem and complete asymptotic analysis, justifying the asymptotics obtained in arXiv:17.01.02867.
In this paper we study the asymptotics of the Korteweg--de Vries (KdV) equation with steplike initial data, which leads to shock waves, in the middle region between the dispersive tail and the soliton region, as $t rightarrow infty$. In our previous
We show that the Cauchy problem for the KdV equation can be solved by the inverse scattering transform (IST) for any initial data bounded from below, decaying sufficiently rapidly at plus infinity, but unrestricted otherwise. Thus our approach doesnt require any boundary condition at minus infinity.
In recent time, by working in a plane with the metric associated with wave equation (the Special Relativity non-definite quadratic form), a complete formalization of space-time trigonometry and a Cauchy-like integral formula have been obtained. In th
In the present manuscript we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the space homogen
An inverse scattering problem for a quantized scalar field ${bm phi}$ obeying a linear Klein-Gordon equation $(square + m^2 + V) {bm phi} = J mbox{in $mathbb{R} times mathbb{R}^3$}$ is considered, where $V$ is a repulsive external potential and $J$ a