B\"acklund transformations for nonlinear evolution equations: Hilbert space approach

TL;DR

This paper introduces a novel Hilbert space method for deriving Bäcklund transformations for nonlinear evolution equations, simplifying the process to solving an abstract Hilbert space equation.

Contribution

The paper presents a new Hilbert space approach to find Bäcklund transformations, advancing the analytical tools for nonlinear evolution equations.

Findings

New Hilbert space method for Bäcklund transformations

Reduction of the problem to an abstract Hilbert space equation

Potential for broader application in nonlinear PDE analysis

Abstract

A new method of determining B\"acklund transformations for nonlinear partial differential equations of the evolution type is introduced. Using the Hilbert space approach the problem of finding B\"acklund transformations is brought down to the solution of an abstract equation in Hilbert space.