Can I read A new method for solving completely integrable PDEs on EtoBox?

A new method for solving completely integrable PDEs by Melnikov, Andrey is a scholarly article available to read on EtoBox.

What is A new method for solving completely integrable PDEs about?

The inverse scattering theory is a basic tool to solve linear differential equations and some Partial Differential Equations (PDEs). Using this theory the Korteweg-de Vries (KdV), the family of evolutionary Non Linear Schrodinger (NLS) equations, Kadomtzev-Petviashvili and many more completely integrable PDEs of mathematical physics are solved, using Zacharv-Shabath scheme. This last approach includes the use of a Lax pair, and has an advantage to be applied to wider class of equations, like difference equations, but has a disadvantage to be used only for "rapidly decreasing solutions". This technique is also intimately related to completely integrable systems. The identifying process of a Lax pair, a system and finally the "scattering data" is usually a difficult process, simplified in many cases by physicals models providing clues of how the scattering data should be chosen. In this work we show that the scattering data can be encoded into singularities of a very special mathematical object: J-unitary, identity at infinity matrix-valued function, which, if evolved once, solves the inverse scattering theory, if evolved twice solves evolutionary PDEs. The provided scheme seems to b

Author

Melnikov, Andrey

Published

2012

Language

EN