Preface -- Contents -- Chapter 1 Linear Quantum Mechanics: Its Successes and Problems -- 1.1 The Fundamental Hypotheses of the Linear Quantum Mechanics -- 1.2 Successes and Problems of the Linear Quantum Mechanics -- 1.3 Dispute between Bohr and Einstein -- 1.4 Analysis on the Roots of Problems of Linear Quantum Mechanics and Review on Recent Developments -- Bibliography -- Chapter 2 Macroscopic Quantum Effects and Motions of Quasi-Particles -- 2.1 Macroscopic Quantum Effects -- 2.1.1 Macroscopic quantum effect in superconductors -- 2.1.2 Macroscopic quantum effect in liquid helium -- 2.1.3 Other macroscopic quantum effects -- 2.2 Analysis on the Nature of Macroscopic Quantum Effect -- 2.3 Motion of Superconducting Electrons -- 2.3.1 Motion of electrons in the absence of external fields -- 2.3.2 Motion of electrons in the presence of an electromagnetic field -- 2.4 Analysis of Macroscopic Quantum Effects in Inhomogeneous Superconductive Systems -- 2.4.1 Proximity effect -- 2.4.2 Josephson current in S-I-S and S-N-S junctions -- 2.4.3 Josephson effect in SNIS junction -- 2.5 Josephson Effect and Transmission of Vortex Lines Along the Superconductive Junctions -- 2.6 Motion of Electrons in Non-Equilibrium Superconductive Systems -- 2.7 Motion of Helium Atoms in Quantum Superfluid -- Bibliography -- Chapter 3 The Fundamental Principles and Theories of Nonlinear Quantum Mechanics -- 3.1 Lessons Learnt from the Macroscopic Quantum Effects -- 3.2 Fundamental Principles of Nonlinear Quantum Mechanics -- 3.3 The Fundamental Theory of Nonlinear Quantum Mechanics -- 3.3.1 Principle of nonlinear superposition and Bäcklund transformation -- 3.3.2 Nonlinear Fourier transformation -- 3.3.3 Method of quantization -- 3.3.4 Nonlinear perturbation theory -- 3.4 Properties of Nonlinear Quantum-Mechanical Systems -- Bibliography.

Chapter 4 Wave-Corpuscle Duality of Microscopic Particles in Nonlinear Quantum Mechanics -- 4.1 Invariance and Conservation Laws, Mass, Momentum and Energy of Microscopic Particles in the Nonlinear Quantum Mechanics -- 4.2 Position of Microscopic Particles and Law of Motion -- 4.3 Collision between Microscopic Particles -- 4.3.1 Attractive interaction (b > 0) -- 4.3.2 Repulsive interaction (b < 0) -- 4.3.3 Numerical simulation -- 4.4 Properties of Elastic Interaction between Microscopic Particles -- 4.5 Mechanism and Rules of Collision between Microscopic Particles -- 4.6 Collisions of Quantum Microscopic Particles -- 4.7 Stability of Microscopic Particles in Nonlinear Quantum Mechanics -- 4.7.1 "Initial" stability -- 4.7.2 Structural stability -- 4.8 Demonstration on Stability of Microscopic Particles -- 4.9 Multi-Particle Collision and Stability in Nonlinear Quantum Mechanics -- 4.10 Transport Properties and Diffusion of Microscopic Particles in Viscous Environment -- 4.11 Microscopic Particles in Nonlinear Quantum Mechanics versus Macroscopic Point Particles -- 4.12 Reflection and Transmission of Microscopic Particles at Interfaces -- 4.13 Scattering of Microscopic Particles by Impurities -- 4.14 Tunneling and Fraunhofer Diffraction -- 4.15 Squeezing Effects of Microscopic Particles Propagating in Nonlinear Media -- 4.16 Wave-corpuscle Duality of Microscopic Particles in a Quasiperiodic Perturbation Potential -- Bibliography -- Chapter 5 Nonlinear Interaction and Localization of Particles -- 5.1 Dispersion Effect and Nonlinear Interaction -- 5.2 Effects of Nonlinear Interactions on Behaviors of Microscopic Particles -- 5.3 Self-Interaction and Intrinsic Nonlinearity -- 5.4 Self-localization of Microscopic Particle by Inertialess Self-interaction -- 5.5 Nonlinear Effect of Media and Self-focusing Mechanism.

5.6 Localization of Exciton and Self-trapping Mechanism -- 5.7 Initial Condition for Localization of Microscopic Particle -- 5.8 Experimental Verification of Localization of Microscopic Particle -- 5.8.1 Observation of nonpropagating surface water soliton in water troughs -- 5.8.2 Experiment on optical solitons in fibers -- Bibliography -- Chapter 6 Nonlinear versus Linear Quantum Mechanics -- 6.1 Nonlinear Quantum Mechanics: An Inevitable Result of Development of Quantum Mechanics -- 6.2 Relativistic Theory and Self-consistency of Nonlinear Quantum Mechanics -- 6.2.1 Bound state and Lorentz relations -- 6.2.2 Interaction between microscopic particles in relativistic theory -- 6.2.3 Relativistic dynamic equations in the nonrelativistic limit -- 6.2.4 Nonlinear Dirac equation -- 6.3 The Uncertainty Relation in Linear and Nonlinear Quantum Mechanics -- 6.3.1 The uncertainty relation in linear quantum mechanics -- 6.3.2 The uncertainty relation in nonlinear quantum mechanics -- 6.4 Energy Spectrum of Hamiltonian and Vector Form of the Non-linear Schrödinger Equation -- 6.4.1 General approach -- 6.4.2 System with two degrees of freedom -- 6.4.3 Perturbative method -- 6.4.4 Vector nonlinear Schrödinger equation -- 6.5 Eigenvalue Problem of the Nonlinear Schrödinger Equation -- 6.6 Microscopic Causality in Linear and Nonlinear Quantum Mechanics -- Bibliography -- Chapter 7 Problem Solving in Nonlinear Quantum Mechanics -- 7.1 Overview of Methods for Solving Nonlinear Quantum Mechanics Problems -- 7.1.1 Inverse scattering method -- 7.1.2 Bäcklund transformation -- 7.1.3 Hirota method -- 7.1.4 Function and variable transformations -- 7.2 Traveling-Wave Methods -- 7.2.1 Nonlinear Schrödinger equation -- 7.2.2 Sine-Gordon equation -- 7.3 Inverse Scattering Method.

7.4 Perturbation Theory Based on the Inverse Scattering Transformation for the Nonlinear Schrödinger Equation -- 7.5 Direct Perturbation Theory in Nonlinear Quantum Mechanics -- 7.5.1 Method of Gorshkov and Ostrovsky -- 7.5.2 Perturbation technique of Bishop -- 7.6 Linear Perturbation Theory in Nonlinear Quantum Mechanics -- 7.6.1 Nonlinear Schrödinger equation -- 7.6.2 Sine-Gordon equation -- 7.7 Nonlinearly Variational Method for the Nonlinear Schrödinger Equation -- 7.8 D Operator and Hirota Method -- 7.9 Bäcklund Transformation Method -- 7.9.1 Auto-Bäcklund transformation method -- 7.9.2 Bäcklund transform of Hirota -- 7.10 Method of Separation of Variables -- 7.11 Solving Higher-Dimensional Equations by Reduction -- Bibliography -- Chapter 8 Microscopic Particles in Different Nonlinear Systems -- 8.1 Charged Microscopic Particles in an Electromagnetic Field -- 8.2 Microscopic Particles Interacting with the Field of an External Traveling Wave -- 8.3 Microscopic Particle in Time-dependent Quadratic Potential -- 8.4 2D Time-dependent Parabolic Potential-field -- 8.5 Microscopic Particle Subject to a Monochromatic Acoustic Wave -- 8.6 Effect of Energy Dissipation on Microscopic Particles -- 8.7 Motion of Microscopic Particles in Disordered Systems -- 8.8 Dynamics of Microscopic Particles in Inhomogeneous Systems -- 8.9 Dynamic Properties of Microscopic Particles in a Random Inhomogeneous Media -- 8.9.1 Mean field method -- 8.9.2 Statistical adiabatic approximation -- 8.9.3 Inverse-scattering transformation based statistical perturbation theory -- 8.10 Microscopic Particles in Interacting Many-particle Systems -- 8.11 Effects of High-order Dispersion on Microscopic Particles -- 8.12 Interaction of Microscopic Particles and Its Radiation Effect in Perturbed Systems with Different Dispersions.

8.13 Microscopic Particles in Three and Two Dimensional Nonlinear Media with Impurities -- Bibliography -- Chapter 9 Nonlinear Quantum-Mechanical Properties of Excitons and Phonons -- 9.1 Excitons in Molecular Crystals -- 9.2 Raman Scattering from Nonlinear Motion of Excitons -- 9.3 Infrared Absorption of Exciton-Solitons in Molecular Crystals -- 9.4 Finite Temperature Excitonic Mössbauer Effect -- 9.5 Nonlinear Excitation of Excitons in Protein -- 9.6 Thermal Stability and Lifetime of Exciton-Soliton at Biological Temperature -- 9.7 Effects of Structural Disorder and Heart Bath on Exciton Localization -- 9.7.1 Effects of structural disorder -- 9.7.2 Influence of heat bath -- 9.8 Eigenenergy Spectra of Nonlinear Excitations of Excitons -- 9.9 Experimental Evidences of Exciton-Soliton State in Molecular Crystals and Protein Molecules -- 9.9.1 Experimental data in acetanilide -- 9.9.2 Infrared and Raman spectra of collagen, E. coli. and human tissue -- 9.9.3 Infrared radiation spectrum of human tissue and Raman spectrum of E. col. -- 9.9.4 Specific heat of ACN and protein -- 9.10 Properties of Nonlinear Excitations of Phonons -- Bibliography -- Chapter 10 Properties of Nonlinear Excitations and Motions of Protons, Polarons and Magnons in Different Systems -- 10.1 Model of Excitation and Proton Transfer in Hydrogen-bonded Systems -- 10.2 Theory of Proton Transferring in Hydrogen Bonded Systems -- 10.3 Thermodynamic Properties and Conductivity of Proton Transfer -- 10.4 Properties of Proton Collective Excitation in Liquid Water -- 10.4.1 States and properties of molecules in liquid water -- 10.4.2 Properties of hydrogen-bonded closed chains in liquid water -- 10.4.3 Ring electric current and mechanism of magnetization of water -- 10.5 Nonlinear Excitation of Polarons and its Properties -- 10.6 Nonlinear Localization of Small Polarons.

10.7 Nonlinear Excitation of Electrons in Coupled Electron-Electron and Electron-Phonon Systems.