About the corollaries of the soliton-breather models of particles tunneling on the example of the nonlinear Klein-Gordon and Schrodinger equation

TL;DR

This paper explores soliton-breather models of particles tunneling using nonlinear Klein-Gordon and Schrödinger equations, revealing spatial restrictions and radiation effects, and introduces a new Schrödinger equation for localized solutions in 3D.

Contribution

It introduces a novel approach to particle tunneling models with nonlinear breathers and proposes a new Schrödinger equation for three-dimensional localized solutions.

Findings

Non-linearity causes spatial restrictions in breather wave properties.

Radiation appears during tunneling due to non-linearity.

A new Schrödinger equation enables solutions localized in 3D space.

Abstract

The paper presents soliton-breather models of particles tunneling on the example of Klein-Gordon and Schrodinger equation nonlinear breathers. It is shown that in this case the non-linearity registration should lead to spatial restrictions in breathers wave properties observation and to appearance of radiation during tunneling. The paper also presents a new type of Schrodinger equation, which leads to the solutions localization in a space three-dimensional spherically symmetric case.