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Nonlinear Differential Equations and Dynamical Systems [[electronic resource] /] / by Ferdinand Verhulst
| Nonlinear Differential Equations and Dynamical Systems [[electronic resource] /] / by Ferdinand Verhulst |
| Autore | Verhulst Ferdinand |
| Edizione | [2nd ed. 1996.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1996 |
| Descrizione fisica | 1 online resource (X, 306 p. 2 illus.) |
| Disciplina | 515/.355 |
| Collana | Universitext |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Dynamics Ergodic theory Physics Statistical physics Dynamical systems Applied mathematics Engineering mathematics Analysis Dynamical Systems and Ergodic Theory Numerical and Computational Physics, Simulation Complex Systems Mathematical and Computational Engineering Statistical Physics and Dynamical Systems |
| ISBN | 3-642-61453-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Introduction -- 1.1 Definitions and notation -- 1.2 Existence and uniqueness -- 1.3 Gronwall’s inequality -- 2 Autonomous equations -- 2.1 Phase-space, orbits -- 2.2 Critical points and linearisation -- 2.3 Periodic solutions -- 2.4 First integrals and integral manifolds -- 2.5 Evolution of a volume element, Liouville’s theorem -- 2.6 Exercises -- 3 Critical points -- 3.1 Two-dimensional linear systems -- 3.2 Remarks on three-dimensional linear systems -- 3.3 Critical points of nonlinear equations -- 3.4 Exercises -- 4 Periodic solutions -- 4.1 Bendixson’s criterion -- 4.2 Geometric auxiliaries, preparation for the Poincaré-Bendixson theorem -- 4.3 The Poincaré-Bendixson theorem -- 4.4 Applications of the Poincaré-Bendixson theorem -- 4.5 Periodic solutions in ?n -- 4.6 Exercises -- 5 Introduction to the theory of stability -- 5.1 Simple examples -- 5.2 Stability of equilibrium solutions -- 5.3 Stability of periodic solutions -- 5.4 Linearisation -- 5.5 Exercises -- 6 Linear Equations -- 6.1 Equations with constant coefficients -- 6.2 Equations with coefficients which have a limit -- 6.3 Equations with periodic coefficients -- 6.4 Exercises -- 7 Stability by linearisation -- 7.1 Asymptotic stability of the trivial solution -- 7.2 Instability of the trivial solution -- 7.3 Stability of periodic solutions of autonomous equations -- 7.4 Exercises -- 8 Stability analysis by the direct method -- 8.1 Introduction -- 8.2 Lyapunov functions -- 8.3 Hamiltonian systems and systems with first integrals -- 8.4 Applications and examples -- 8.5 Exercises -- 9 Introduction to perturbation theory -- 9.1 Background and elementary examples -- 9.2 Basic material -- 9.3 Naïve expansion -- 9.4 The Poincaré expansion theorem -- 9.5 Exercises -- 10 The Poincaré-Lindstedt method -- 10.1 Periodic solutions of autonomous second-order equations -- 10.2 Approximation of periodic solutions on arbitrary long time-scales -- 10.3 Periodic solutions of equations with forcing terms -- 10.4 The existence of periodic solutions -- 10.5 Exercises -- 11 The method of averaging -- 11.1 Introduction -- 11.2 The Lagrange standard form -- 11.3 Averaging in the periodic case -- 11.4 Averaging in the general case -- 11.5 Adiabatic invariants -- 11.6 Averaging over one angle, resonance manifolds -- 11.7 Averaging over more than one angle, an introduction -- 11.8 Periodic solutions -- 11.9 Exercises -- 12 Relaxation Oscillations -- 12.1 Introduction -- 12.2 Mechanical systems with large friction -- 12.3 The van der Pol-equation -- 12.4 The Volterra-Lotka equations -- 12.5 Exercises -- 13 Bifurcation Theory -- 13.1 Introduction -- 13.2 Normalisation -- 13.3 Averaging and normalisation -- 13.4 Centre manifolds -- 13.5 Bifurcation of equilibrium solutions and Hopf bifurcation -- 13.6 Exercises -- 14 Chaos -- 14.1 Introduction and historical context -- 14.2 The Lorenz-equations -- 14.3 Maps associated with the Lorenz-equations -- 14.4 One-dimensional dynamics -- 14.5 One-dimensional chaos: the quadratic map -- 14.6 One-dimensional chaos: the tent map -- 14.7 Fractal sets -- 14.8 Dynamical characterisations of fractal sets -- 14.9 Lyapunov exponents -- 14.10 Ideas and references to the literature -- 15 Hamiltonian systems -- 15.1 Introduction -- 15.2 A nonlinear example with two degrees of freedom -- 15.3 Birkhoff-normalisation -- 15.4 The phenomenon of recurrence -- 15.5 Periodic solutions -- 15.6 Invariant tori and chaos -- 15.7 The KAM theorem -- 15.8 Exercises -- Appendix 1: The Morse lemma -- Appendix 2: Linear periodic equations with a small parameter -- Appendix 3: Trigonometric formulas and averages -- Appendix 4: A sketch of Cotton’s proof of the stable and unstable manifold theorem 3.3 -- Appendix 5: Bifurcations of self-excited oscillations -- Appendix 6: Normal forms of Hamiltonian systems near equilibria -- Answers and hints to the exercises -- References. |
| Record Nr. | UNINA-9910480045903321 |
Verhulst Ferdinand
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nonlinear Differential Equations and Dynamical Systems [[electronic resource] /] / by Ferdinand Verhulst
| Nonlinear Differential Equations and Dynamical Systems [[electronic resource] /] / by Ferdinand Verhulst |
| Autore | Verhulst Ferdinand |
| Edizione | [2nd ed. 1996.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1996 |
| Descrizione fisica | 1 online resource (X, 306 p. 2 illus.) |
| Disciplina | 515/.355 |
| Collana | Universitext |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Dynamics Ergodic theory Physics Statistical physics Dynamical systems Applied mathematics Engineering mathematics Analysis Dynamical Systems and Ergodic Theory Numerical and Computational Physics, Simulation Complex Systems Mathematical and Computational Engineering Statistical Physics and Dynamical Systems |
| ISBN | 3-642-61453-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Introduction -- 1.1 Definitions and notation -- 1.2 Existence and uniqueness -- 1.3 Gronwall’s inequality -- 2 Autonomous equations -- 2.1 Phase-space, orbits -- 2.2 Critical points and linearisation -- 2.3 Periodic solutions -- 2.4 First integrals and integral manifolds -- 2.5 Evolution of a volume element, Liouville’s theorem -- 2.6 Exercises -- 3 Critical points -- 3.1 Two-dimensional linear systems -- 3.2 Remarks on three-dimensional linear systems -- 3.3 Critical points of nonlinear equations -- 3.4 Exercises -- 4 Periodic solutions -- 4.1 Bendixson’s criterion -- 4.2 Geometric auxiliaries, preparation for the Poincaré-Bendixson theorem -- 4.3 The Poincaré-Bendixson theorem -- 4.4 Applications of the Poincaré-Bendixson theorem -- 4.5 Periodic solutions in ?n -- 4.6 Exercises -- 5 Introduction to the theory of stability -- 5.1 Simple examples -- 5.2 Stability of equilibrium solutions -- 5.3 Stability of periodic solutions -- 5.4 Linearisation -- 5.5 Exercises -- 6 Linear Equations -- 6.1 Equations with constant coefficients -- 6.2 Equations with coefficients which have a limit -- 6.3 Equations with periodic coefficients -- 6.4 Exercises -- 7 Stability by linearisation -- 7.1 Asymptotic stability of the trivial solution -- 7.2 Instability of the trivial solution -- 7.3 Stability of periodic solutions of autonomous equations -- 7.4 Exercises -- 8 Stability analysis by the direct method -- 8.1 Introduction -- 8.2 Lyapunov functions -- 8.3 Hamiltonian systems and systems with first integrals -- 8.4 Applications and examples -- 8.5 Exercises -- 9 Introduction to perturbation theory -- 9.1 Background and elementary examples -- 9.2 Basic material -- 9.3 Naïve expansion -- 9.4 The Poincaré expansion theorem -- 9.5 Exercises -- 10 The Poincaré-Lindstedt method -- 10.1 Periodic solutions of autonomous second-order equations -- 10.2 Approximation of periodic solutions on arbitrary long time-scales -- 10.3 Periodic solutions of equations with forcing terms -- 10.4 The existence of periodic solutions -- 10.5 Exercises -- 11 The method of averaging -- 11.1 Introduction -- 11.2 The Lagrange standard form -- 11.3 Averaging in the periodic case -- 11.4 Averaging in the general case -- 11.5 Adiabatic invariants -- 11.6 Averaging over one angle, resonance manifolds -- 11.7 Averaging over more than one angle, an introduction -- 11.8 Periodic solutions -- 11.9 Exercises -- 12 Relaxation Oscillations -- 12.1 Introduction -- 12.2 Mechanical systems with large friction -- 12.3 The van der Pol-equation -- 12.4 The Volterra-Lotka equations -- 12.5 Exercises -- 13 Bifurcation Theory -- 13.1 Introduction -- 13.2 Normalisation -- 13.3 Averaging and normalisation -- 13.4 Centre manifolds -- 13.5 Bifurcation of equilibrium solutions and Hopf bifurcation -- 13.6 Exercises -- 14 Chaos -- 14.1 Introduction and historical context -- 14.2 The Lorenz-equations -- 14.3 Maps associated with the Lorenz-equations -- 14.4 One-dimensional dynamics -- 14.5 One-dimensional chaos: the quadratic map -- 14.6 One-dimensional chaos: the tent map -- 14.7 Fractal sets -- 14.8 Dynamical characterisations of fractal sets -- 14.9 Lyapunov exponents -- 14.10 Ideas and references to the literature -- 15 Hamiltonian systems -- 15.1 Introduction -- 15.2 A nonlinear example with two degrees of freedom -- 15.3 Birkhoff-normalisation -- 15.4 The phenomenon of recurrence -- 15.5 Periodic solutions -- 15.6 Invariant tori and chaos -- 15.7 The KAM theorem -- 15.8 Exercises -- Appendix 1: The Morse lemma -- Appendix 2: Linear periodic equations with a small parameter -- Appendix 3: Trigonometric formulas and averages -- Appendix 4: A sketch of Cotton’s proof of the stable and unstable manifold theorem 3.3 -- Appendix 5: Bifurcations of self-excited oscillations -- Appendix 6: Normal forms of Hamiltonian systems near equilibria -- Answers and hints to the exercises -- References. |
| Record Nr. | UNINA-9910789217203321 |
|
Verhulst Ferdinand
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nonlinear Differential Equations and Dynamical Systems [[electronic resource] /] / by Ferdinand Verhulst
| Nonlinear Differential Equations and Dynamical Systems [[electronic resource] /] / by Ferdinand Verhulst |
| Autore | Verhulst Ferdinand |
| Edizione | [2nd ed. 1996.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1996 |
| Descrizione fisica | 1 online resource (X, 306 p. 2 illus.) |
| Disciplina | 515/.355 |
| Collana | Universitext |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Dynamics Ergodic theory Physics Statistical physics Dynamical systems Applied mathematics Engineering mathematics Analysis Dynamical Systems and Ergodic Theory Numerical and Computational Physics, Simulation Complex Systems Mathematical and Computational Engineering Statistical Physics and Dynamical Systems |
| ISBN | 3-642-61453-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Introduction -- 1.1 Definitions and notation -- 1.2 Existence and uniqueness -- 1.3 Gronwall’s inequality -- 2 Autonomous equations -- 2.1 Phase-space, orbits -- 2.2 Critical points and linearisation -- 2.3 Periodic solutions -- 2.4 First integrals and integral manifolds -- 2.5 Evolution of a volume element, Liouville’s theorem -- 2.6 Exercises -- 3 Critical points -- 3.1 Two-dimensional linear systems -- 3.2 Remarks on three-dimensional linear systems -- 3.3 Critical points of nonlinear equations -- 3.4 Exercises -- 4 Periodic solutions -- 4.1 Bendixson’s criterion -- 4.2 Geometric auxiliaries, preparation for the Poincaré-Bendixson theorem -- 4.3 The Poincaré-Bendixson theorem -- 4.4 Applications of the Poincaré-Bendixson theorem -- 4.5 Periodic solutions in ?n -- 4.6 Exercises -- 5 Introduction to the theory of stability -- 5.1 Simple examples -- 5.2 Stability of equilibrium solutions -- 5.3 Stability of periodic solutions -- 5.4 Linearisation -- 5.5 Exercises -- 6 Linear Equations -- 6.1 Equations with constant coefficients -- 6.2 Equations with coefficients which have a limit -- 6.3 Equations with periodic coefficients -- 6.4 Exercises -- 7 Stability by linearisation -- 7.1 Asymptotic stability of the trivial solution -- 7.2 Instability of the trivial solution -- 7.3 Stability of periodic solutions of autonomous equations -- 7.4 Exercises -- 8 Stability analysis by the direct method -- 8.1 Introduction -- 8.2 Lyapunov functions -- 8.3 Hamiltonian systems and systems with first integrals -- 8.4 Applications and examples -- 8.5 Exercises -- 9 Introduction to perturbation theory -- 9.1 Background and elementary examples -- 9.2 Basic material -- 9.3 Naïve expansion -- 9.4 The Poincaré expansion theorem -- 9.5 Exercises -- 10 The Poincaré-Lindstedt method -- 10.1 Periodic solutions of autonomous second-order equations -- 10.2 Approximation of periodic solutions on arbitrary long time-scales -- 10.3 Periodic solutions of equations with forcing terms -- 10.4 The existence of periodic solutions -- 10.5 Exercises -- 11 The method of averaging -- 11.1 Introduction -- 11.2 The Lagrange standard form -- 11.3 Averaging in the periodic case -- 11.4 Averaging in the general case -- 11.5 Adiabatic invariants -- 11.6 Averaging over one angle, resonance manifolds -- 11.7 Averaging over more than one angle, an introduction -- 11.8 Periodic solutions -- 11.9 Exercises -- 12 Relaxation Oscillations -- 12.1 Introduction -- 12.2 Mechanical systems with large friction -- 12.3 The van der Pol-equation -- 12.4 The Volterra-Lotka equations -- 12.5 Exercises -- 13 Bifurcation Theory -- 13.1 Introduction -- 13.2 Normalisation -- 13.3 Averaging and normalisation -- 13.4 Centre manifolds -- 13.5 Bifurcation of equilibrium solutions and Hopf bifurcation -- 13.6 Exercises -- 14 Chaos -- 14.1 Introduction and historical context -- 14.2 The Lorenz-equations -- 14.3 Maps associated with the Lorenz-equations -- 14.4 One-dimensional dynamics -- 14.5 One-dimensional chaos: the quadratic map -- 14.6 One-dimensional chaos: the tent map -- 14.7 Fractal sets -- 14.8 Dynamical characterisations of fractal sets -- 14.9 Lyapunov exponents -- 14.10 Ideas and references to the literature -- 15 Hamiltonian systems -- 15.1 Introduction -- 15.2 A nonlinear example with two degrees of freedom -- 15.3 Birkhoff-normalisation -- 15.4 The phenomenon of recurrence -- 15.5 Periodic solutions -- 15.6 Invariant tori and chaos -- 15.7 The KAM theorem -- 15.8 Exercises -- Appendix 1: The Morse lemma -- Appendix 2: Linear periodic equations with a small parameter -- Appendix 3: Trigonometric formulas and averages -- Appendix 4: A sketch of Cotton’s proof of the stable and unstable manifold theorem 3.3 -- Appendix 5: Bifurcations of self-excited oscillations -- Appendix 6: Normal forms of Hamiltonian systems near equilibria -- Answers and hints to the exercises -- References. |
| Record Nr. | UNINA-9910807088203321 |
|
Verhulst Ferdinand
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
A Toolbox of Averaging Theorems [[electronic resource] ] : Ordinary and Partial Differential Equations / / by Ferdinand Verhulst
| A Toolbox of Averaging Theorems [[electronic resource] ] : Ordinary and Partial Differential Equations / / by Ferdinand Verhulst |
| Autore | Verhulst Ferdinand |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (199 pages) |
| Disciplina | 515.35 |
| Collana | Surveys and Tutorials in the Applied Mathematical Sciences |
| Soggetto topico |
Differential equations
Engineering mathematics Differential Equations Engineering Mathematics |
| ISBN | 3-031-34515-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Perturbation Problems -- 1.2 Amplitude-Phase Transformation -- 1.3 Comoving Varables -- 1.4 Amplitude-Angle Transformation -- 1.5 Perturbed Linear Systems and Forcing -- 1.6 Order Functions and Timescales -- 1.7 On Contraction and Iteration Approximations -- 1.8 Comparison of Methods -- 1.9 Analytic and Numerical Approximations -- 2 First Order Periodic Averaging -- 2.1 The Basic Averaging Theorem -- 2.2 Quasi-Periodic Averaging -- 2.3 Applications -- 2.3.1 A Linear Example with Forcing -- 2.3.2 The Van der Pol-Equation -- 2.3.3 Averaging Autonomous Equations -- 2.3.4 A Generalised Van der Pol-Equation -- 2.3.5 The Mathieu-Equation with Damping -- 2.3.6 The Forced Duffing-Equation Without Damping -- 2.3.7 Nonlinear Damping -- 2.3.8 A Hamiltonian System with Cubic Term -- 2.3.9 The Spring-Pendulum -- 3 Periodic Solutions -- 3.1 Periodic Solutions -- 3.2 Applications -- 3.2.1 A First Order Equation -- 3.2.2 A Generalised Van der Pol-Equation -- 3.2.3 The Duffing-Equation with Small Forcing -- 3.2.4 The Nonlinear Mathieu-Equation -- 3.2.5 The Mathieu-Equation with Damping -- 3.2.6 Models for Autoparametric Energy Absorption -- 3.3 The Poincaré-Lindstedt Method -- 3.3.1 General Approach for Variational Systems -- 3.3.2 The Poincaré-Lindstedt Approach for Autonomous Systems -- 3.3.3 The Poincaré-Lindstedt Approach for Non-autonomous Systems -- 3.4 Applications of the Poincaré-Lindstedt Method -- 3.4.1 The Periodic Solution of the Van der Pol-Equation -- 3.4.2 A Case of Non-uniqueness -- 3.4.3 The Mathieu-Equation -- 4 Second Order Periodic Averaging -- 4.1 Second Order Precision -- 4.2 Applications -- 4.2.1 Simple Conservative Systems -- 4.2.2 Van der Pol-Excitation at 2nd Order -- 4.2.3 Intermezzo on the Nature of Timescales -- 4.2.4 The Chaotic Systems Sprott A and NE8.
5 First Order General Averaging -- 5.1 The Basic Theorem for General Averaging -- 5.2 Second Order General Averaging -- 5.3 Applications -- 5.3.1 Van der Pol-Equation with Changing Friction -- 5.3.2 Linear Oscillations with Increasing Friction, Adiabatic Invariant -- 5.3.3 Quasi-Periodic Forcing of the Duffing-Equation -- 5.3.4 Quasi-Periodic Forcing of a Van der Pol Limit Cycle -- 5.3.5 Evolution to Symmetry, Adiabatic Invariants -- 6 Approximations on Timescales Longer than 1/ -- 6.1 When First Order Periodic Averaging Produces Trivial Results -- 6.2 The Case of Attraction -- 6.3 Applications -- 6.3.1 Excitation Frequency ω=1 for the Mathieu-Equation -- 6.3.2 A Cubic Hamiltonian System in 1:1 Resonance -- 6.3.3 The Amplitude of Periodic Solutions of Autonomous Equations -- 6.3.4 The Damped Duffing Equation with O(1) Forcing -- 7 Averaging over Spatial Variables -- 7.1 Averaging over One Angle -- 7.2 Averaging over More Angles -- 7.3 Applications -- 7.3.1 A Pendulum with Slow Time Frequency Variation -- 7.3.2 A Typical Problem with One Resonance Manifold -- 7.3.3 Behaviour in a Resonance Manifold -- 7.3.4 A 3-Dimensional System with 2 Angles -- 7.3.5 Intersection of Resonance Manifolds -- 7.3.6 A Rotating Flywheel on an Elastic Foundation -- 8 Hamiltonian Resonances -- 8.1 Frequencies and Resonances in the Hamiltonian Case -- 8.2 Higher Order Resonance in 2 Degrees-of-Freedom -- 8.3 The Poincaré Recurrence Theorem -- 8.4 Applications -- 8.4.1 A General Cubic Potential -- 8.4.2 A Cubic Potential in Higher Order Resonance -- 8.4.3 The Spring-Pendulum in Higher Order Resonance -- 8.4.4 Three dof, the 1:2:1 Resonance -- 8.4.5 The Fermi-Pasta-Ulam Chain -- 8.4.6 Interaction of Low and Higher Order, the 2:2:3 Resonance -- 8.4.7 Interaction of Low and Higher Order, the 1:1:4 Resonance -- 9 Quasi-Periodic Solutions and Tori. 9.1 Tori by Bogoliubov-Mitropolsky-Hale Continuation -- 9.2 The Case of Parallel Flow -- 9.3 Tori Created by Neimark-Sacker Bifurcation -- 9.4 Applications -- 9.4.1 A Forced Van der Pol-Oscillator -- 9.4.2 Quasi-Periodic Solutions in the Forced Van der Pol-Equation -- 9.4.3 Neimark-Sacker Bifurcation in Two Coupled Oscillators -- 9.4.4 Interaction of Vibrations and Parametric Excitation -- 9.4.5 Interaction of Self-Excited and Parametric Excitation -- 9.4.6 Interaction of Self-Excited Oscillations (Hale's Example) -- 9.5 Iteration by Integral Equations -- 9.6 Applications of the Iteration Procedure -- 9.6.1 Hale's Example by Iteration -- 9.6.2 Two Coupled Oscillators with Forcing -- 9.6.3 Iteration of the Cartoon Problem -- 10 Averaging for Partial Differential Equations -- 10.1 Metric Spaces and Norms, a Reminder -- 10.2 Averaging a Linear Operator -- 10.3 Wave Equations, Projection Methods -- 10.4 Applications -- 10.4.1 Application to a Time-Periodic Advection-Diffusion Problem -- 10.4.2 Advection-Diffusion with Reactions and Sources -- 10.4.3 The Wave Equation with Cubic Nonlinearity -- 10.4.4 A 1-Dimensional Dispersive, Cubic Klein-Gordon Equation -- 10.4.5 The Cubic Klein-Gordon Equation on a Square -- 10.4.6 The Keller-Kogelman Problem -- 10.4.7 A Parametrically Excited Linear Wave Equation -- 10.4.8 Parametrical Excitation of Nonlinear Waves -- 10.4.9 Parametrical Excitation of 2-Dimensional Nonlinear Waves -- References -- Index. |
| Record Nr. | UNINA-9910735788103321 |
|
Verhulst Ferdinand
|
||
| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||