Asymptotic perturbation methods : for nonlinear differential equations in physics / / Attilio Maccari

• Record Nr.: UNINA9910830136703321
• Autore: Maccari Attilio
• Pubbl/distr/stampa: Weinheim, Germany : , : Wiley-VCH GmbH, , [2023]; ©2023
• ISBN: 9783527841721; 9783527414215
• Descrizione fisica: 1 online resource (256 pages)
• Disciplina: 381
• Soggetti: Differential equations, Partial
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover -- Title Page -- Copyright -- Contents -- About the Author -- Foreword -- Introduction -- Chapter 1 The Asymptotic Perturbation Method for Nonlinear Oscillators -- 1.1 Introduction -- 1.2 Nonlinear Dynamical Systems -- 1.3 The Approximate Solution -- 1.4 Comparison with the Results of the Numerical Integration -- 1.5 External Excitation in Resonance with the Oscillator -- 1.6 Conclusion -- Chapter 2 The Asymptotic Perturbation Method for Remarkable Nonlinear Systems -- 2.1 Introduction -- 2.2 Periodic Solutions and Their Stability -- 2.3 Global Analysis of the Model System -- 2.4 Infinite‐period Symmetric Homoclinic Bifurcation -- 2.5 A Few Considerations -- 2.6 A Peculiar Quasiperiodic Attractor -- 2.7 Building an Approximate Solution -- 2.8 Results from Numerical Simulation -- 2.9 Conclusion -- Chapter 3 The Asymptotic Perturbation Method for Vibration Control with Time‐delay State Feedback -- 3.1 Introduction -- 3.2 Time‐delay State Feedback -- 3.3 The Perturbation Method -- 3.4 Stability Analysis and Parametric Resonance Control -- 3.4.1 The Frequency-Response Curve Is -- 3.5 Suppression of the Two‐period Quasiperiodic Motion -- 3.6 Vibration Control for Other Nonlinear Systems -- Chapter 4 The Asymptotic Perturbation Method for Vibration Control by Nonlocal Dynamics -- 4.1 Introduction -- 4.2 Vibration Control for the van der Pol Equation -- 4.3 Stability Analysis and Parametric Resonance Control -- 4.4 Suppression of the Two‐; period Quasiperiodic Motion -- 4.5 Conclusion -- Chapter 5 The Asymptotic Perturbation Method for Nonlinear Continuous Systems -- 5.1 Introduction -- 5.2 The Approximate Solution for the Primary Resonance of the nth Mode -- 5.3 The Approximate Solution for the Subharmonic Resonance of Order One‐half of the nth Mode -- 5.4 Conclusion.; Chapter 6 The Asymptotic Perturbation Method for Dispersive Nonlinear Partial Differential Equations -- 6.1 Introduction -- 6.2 Model Nonlinear PDES Obtained from the Kadomtsev-Petviashvili Equation -- 6.3 The Lax Pair for the Model Nonlinear PDE -- 6.4 A Few Remarks -- 6.5 A Generalized Hirota Equation in 2 + 1 Dimensions -- 6.6 Model Nonlinear PDEs Obtained from the KP Equation -- 6.7 The Lax Pair for the Hirota-Maccari Equation -- 6.8 Conclusion -- Chapter 7 The Asymptotic Perturbation Method for Physics Problems -- 7.1 Introduction -- 7.2 Derivation of the Model System -- 7.3 Integrability of the Model System of Equations -- 7.4 Exact Solutions for the C‐integrable Model Equation -- 7.4.1 Nonlinear Wave -- 7.4.2 Solitons -- 7.4.3 Dromions -- 7.4.4 Lumps -- 7.4.5 Ring Solitons -- 7.4.6 Instantons -- 7.4.7 Moving Breather‐Like Structures -- 7.5 Conclusion -- Chapter 8 The Asymptotic Perturbation Model for Elementary Particle Physics -- 8.1 Introduction -- 8.2 Derivation of the Model System -- 8.3 Integrability of the Model System of Equations -- 8.4 Exact Solutions for the C‐integrable Model Equation -- 8.4.1 Nonlinear Wave -- 8.4.2 Solitons -- 8.4.3 Dromions -- 8.4.4 Lumps -- 8.4.5 Ring Solitons -- 8.4.6 Instantons -- 8.4.7 Moving Breather‐like Structures -- 8.5 A Few Considerations -- 8.6 Hidden Symmetry Models -- 8.7 Derivation of the Model System -- 8.8 Coherent Solutions -- 8.8.1 Nonlinear Wave -- 8.8.2 Solitons -- 8.8.3 Dromions -- 8.8.4 Lumps -- 8.8.5 Ring Solitons -- 8.8.6 Instantons -- 8.8.7 Moving Breather‐like Structures -- 8.9 Chaotic and Fractal Solutions -- 8.9.1 Chaotic-Chaotic and Chaotic-Periodic Patterns -- 8.9.2 Chaotic Line Soliton Solutions -- 8.9.3 Chaotic Dromion and Lump Patterns -- 8.9.4 Nonlocal Fractal Solutions -- 8.9.5 Fractal Dromion and Lump Solutions -- 8.9.6 Stochastic Fractal Dromion and Lump Excitations.; 8.10 Conclusion -- Chapter 9 The Asymptotic Perturbation Method for Rogue Waves -- 9.1 Introduction -- 9.2 The Mathematical Framework -- 9.3 The Maccari System -- 9.4 Rogue Wave Physical Explanation According to the Maccari System and Blowing Solutions -- 9.5 Conclusion -- Chapter 10 The Asymptotic Perturbation Method for Fractal and Chaotic Solutions -- 10.1 Introduction -- 10.2 A New Integrable System from the Dispersive Long‐wave Equation -- 10.3 Nonlinear Coherent Solutions -- 10.3.1 Nonlinear Wave -- 10.3.2 Solitons -- 10.3.3 Dromions -- 10.3.4 Lumps -- 10.3.5 Ring Solitons -- 10.3.6 Instantons -- 10.3.7 Moving Breather‐Like Structures -- 10.4 Chaotic and Fractal Solutions -- 10.4.1 Chaotic-Chaotic and Chaotic-Periodic Patterns -- 10.4.2 Chaotic Line Soliton Solutions -- 10.4.3 Chaotic Dromion and Lump Patterns -- 10.4.4 Nonlocal Fractal Solutions -- 10.4.5 Fractal Dromion and Lump Solutions -- 10.4.6 Stochastic Fractal Excitations -- 10.4.7 Stochastic Fractal Dromion and Lump Excitations -- 10.5 Conclusion -- Chapter 11 The Asymptotic Perturbation Method for Nonlinear Relativistic and Quantum Physics -- 11.1 Introduction -- 11.2 The NLS Equation for a1 &gt -- 0 -- 11.3 The NLS Equation for a1 &lt -- 0 -- 11.4 A Possible Extension -- 11.5 The Nonrelativistic Case -- 11.6 The Relativistic Case -- 11.7 Conclusion -- Chapter 12 Cosmology -- 12.1 Introduction -- 12.2 A New Field Equation -- 12.3 Exact Solution in the Robertson-Walker Metrics -- 12.4 Entropy Production -- 12.5 Conclusion -- Chapter 13 Confinement and Asymptotic Freedom in a Purely Geometric ; Framework -- 13.1 Introduction -- 13.2 The Uncertainty Principle -- 13.3 Confinement and Asymptotic Freedom for the Strong Interaction -- 13.4 The Motion of a Light Ray Into a Hadron -- 13.5 Conclusion.; Chapter 14 The Asymptotic Perturbation Method for a Reverse Infinite‐Period Bifurcation in the Nonlinear Schrodinger Equation -- 14.1 Introduction -- 14.2 Building an Approximate Solution -- 14.3 A Reverse Infinite‐Period Bifurcation -- 14.4 Conclusion -- Conclusion -- References -- Index -- EULA.