Classical and SUSY solutions of the Boiti–Leon–Manna–Pempinelli equation

Solutions of the classical Yang-Baxter equation and noncommutative deformations

In this paper, I will show that, if a Lie algebra G acts on a manifold P , any solution of the classical Yang-Baxter equation on G gives arise to a Poisson tensor on P and a torsion-free and flat contravariant connection (with respect to the Poisson tensor). Moreover, if the action is locally free, the matacurvature of the above contravariant connection vanishes. This will permit to get a large...

Acoustic Limit of the Boltzmann Equation: Classical Solutions

We study the acoustic limit from the Boltzmann equation in the framework of classical solutions. For a solution Fε = μ+ε √ μfε to the rescaled Boltzmann equation in the acoustic time scaling ∂tFε + v·∇xFε = 1 ε Q(Fε, Fε) , inside a periodic box T, we establish the global-in-time uniform energy estimates of fε in ε and prove that fε converges strongly to f whose dynamics is governed by the acous...

Diagonal and Monomial Solutions of the Matrix Equation AXB=C

In this article, we consider the matrix equation $AXB=C$, where A, B, C are given matrices and give new necessary and sufficient conditions for the existence of the diagonal solutions and monomial solutions to this equation. We also present a general form of such solutions. Moreover, we consider the least squares problem $min_X |C-AXB |_F$ where $X$ is a diagonal or monomial matrix. The explici...

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION

New exact solutions for the classical Drinfel'd-Sokolov-Wilson equation

In this paper, we have established new exact analytical solutions for the classical nonlinear Drinfel’d-SokolovWilson equation (DSWE) by using the first integral method. Many periodic, solitonic, and rational solutions have been found. The results revealed remarkable relations of solitary pattern, periodic solutions or solitons. It is shown that this method is effective and direct one, based on...