Mathematical Modeling of Soliton's Evolution in Generalized Quantum Hydrodynamics

TL;DR

This paper develops a unified non-local physical framework that models soliton evolution within generalized quantum hydrodynamics, extending classical kinetic theories to include quantum effects.

Contribution

It introduces a novel approach to modeling solitons in quantum hydrodynamics using generalized Boltzmann kinetics, expanding the theoretical understanding of non-local quantum transport.

Findings

Solitons emerge as natural formations in the generalized quantum hydrodynamics framework.

The theory unifies classical and quantum transport processes.

Extension of Boltzmann kinetics to include quantum effects.

Abstract

This paper addresses the fundamental principles of generalized Boltzmann physical kinetics, as a part of non-local physics. It is shown that the theory of transport processes (including quantum mechanics) can be considered in the frame of unified theory based on the non-local physical description. The paper can be considered also as comments and prolongation of the materials published in the known author's monograph (Boris V. Alexeev, Generalized Boltzmann Physical Kinetics. Elsevier. 2004). The theory leads to solitons as typical formations in the generalized quantum hydrodynamics.