Surjectivity of partial differential operators with good fundamental solutions

FUNDAMENTAL SOLUTIONS OF PSEUDO-DIFFERENTIAL OPERATORS OVER p−ADIC FIELDS

We show the existence of fundamental solutions for p−adic pseudodifferential operators with polynomial symbols.

Fundamental Solutions: Ii-matrix Operators

In this tutorial, we will continue the discussion, started in the tutorial 4, about the derivation of the fundamental solutions. In the former tutorial, we presented techniques for setting up the fundamental solution for simple and compound operators. Herein, we will discuss the use of operator decoupling technique to breakdown matrix operators to simple or compound scalar ones. This method is ...

Topological soliton solutions of the some nonlinear partial differential equations

In this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (SRLW) equation and the (3+1)-dimensional shallow water wave equations. Solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Note t...

Commutative Partial Differential Operators

In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions that may suggest a theory to be developed. In particular, we address the existence of a “spectral variety” generalizing the spectral curve of the one dimension...

Fundamental Solutions of Cubic Operators In