A review of the multiple scale and reductive perturbation methods for deriving uncoupled nonlinear evolution equations. Wave Motion,7, Frankel and T. Relative phase behavior of two slowly coupled oscillators. Federson and J. Non-periodic averaging principles for measure functional differential equations and functional dynamic equations on time scales involving impulses. Differential Equat 10 On the method of matched asymptotic expansions. Parts I-III. Cambridge Phil. A note on Kaplun limits and double asymptotics.

Geometric optics approach to reaction-diffusion equations.

## Asymptotic Analysis

Application of the averaging method to the gyrokinetic plasma. Slow periodic motions with internal sliding modes in variable structure systems. J Control, 75 7 Fu and P. WKB method with repeated roots and its application to the buckling analysis of an everted cylindrical tube. Fruchard and R. Classification of resonant equations. Composite asymptotic expansions and turning points of singularly perturbed ordinary differential equations. Comptes Rendus Math. Composite Asymptotic Expansions, volume of Lect. Use of the averaging method in control problems. Differential Equat.

Complex Analysis.

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Guckenheimer and P. Greenspan and P. Repeated resonance and homoclinic bifurcation in a periodically forced family of oscillators.

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Gingold and P. Asymptotic solutions of a Hamiltonian system in intervals with several turning points. The method of averaging and domains of stability for integral manifolds. A high order generalized method of averaging. A method for incorporating transcendentally small terms into the method of matched asymptotic expansions. Studies in. Applications Math. Gao and V. Introduction to Asymptotic Methods. CRC Press. Grasman and B. A variational approach to singularly perturbed boundary value problems for ordinary and partial differential equations with turning points.

Gaitsgory and M. Averaging of three time scale singularly perturbed control systems.

Multiscale singularly perturbed control systems: limit occupational measures sets and averaging J. Contr Optim. Gu, N. Nefedov, and R. On singular singularly perturbed initial value problems. Lectures on phase transitions and the renormalization group - Goldenfeld, N.

Frontiers in physics, Limits of nonlinear discrete-time control systems with fast subsystems.

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On nonlinear control systems with multiple time scales. Dyn Contr. On the motion of waves in a variable canal of small depth and width De Groen. Spectral properties of second-order singularly perturbed boundary value problems with turning points. The nature of resonance in a singular perturbation problem of turning point type.

An averaging theorem for a perturbed KdV equation. Godin and B. On the determination of the boundary impedance from the far field pattern. Ghil and G. Non-hamiltonian perturbations of integrable systems and resonance trapping. Phase shift modulations for stable, oscillatory, traveling, strongly nonlinear waves. Standard form and a method of averaging for strongly nonlinear oscillatory dispersive traveling waves. Quantum Theory for Mathematicians. Nayfeh S.

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The method of multiple scales and non-linear dispersive waves. On a perturbation theory using Lie transforms. Perturbation Methods. Hagedorn and A. A time-dependent Born-Oppenheimer approximation with exponentially small error estimates. Haario and L. Model reductions and identifications for multiphase phenomena. Harkin, T. Kaper, and A. Coupled pulsation and translation of two gas bubbles in a liquid. Handelman, J. Keller, and R. Loss of boundary conditions in the asymptotic solution of linear ordinary differential equations, I eigenvalue problems.

Hastings, C. Lu, and A. A boundary value problem with multiple solutions from the theory of laminar flow. Henrard and K. Averaging and bifurcations in symmetric systems. Hastings and J. An elementary approach to a model problem of Lagerstrom. The method of multiple scales.

Analysis of some problems having matched asymptotic expansion solutions. Exponential asymptotics and boundary-value problems: keeping both sides happy at all orders.

A turning point problem for a system of linear ordinary differential equations of the third order. Hunter, M. Tajdari, and S. Huveneers and F. A metaphor for adiabatic evolution to symmetry. A remark on singular perturbation methods. Hiroshima Math. Solution of reduced equations derived with singular perturbation methods. Introduction to the method of multiple scales pages Method of multiple scales in quantum optics.

On certain approximate solutions of linear differential equations of the second order. London Math. De Jager and J. The Theory of Singular Perturbations. Jin, P. Markowich, and C. Acta Numer. Singular Perturbation Theory. On the algebraic fundamentals of singular perturbation theory.

Conditions for sustained resonance. Necessary conditions for sustained re-entry roll resonance. Krylov and N. Introduction to Nonlinear Mechanics. Kevorkian and J. Multiple Scale and Singular Perturbation Methods. Von Zeipel method and the two-variable expansion procedure. Perturbation techniques for oscillatory systems with slowly varying coefficients.

Averaging in dynamical systems and large deviations. Averaging and climate models. In Stochastic Climate Models, pages Yu 2 diffusion approximation for slow motion in averaging. Averaging principle for fully coupled dynamical systems and large deviations. Ergodic Theory Dyn. Some recent advances in averaging. In Modern Dynamical Systems and Applications, pages Convergence, nonconvergence and adiabatic transitions in fully coupled averaging.

The renormalization group: a perturbation method for the graduate curriculum. Kreiss and J. Manifolds of slow solutions for highly oscillatory problems.

Indiana Univ. On the existence of slow manifolds for problems with different timescales. Philosophical Transactions: Physical Sciences and Engineering, On the distribution of the maximum number of broken machines for the repairman problem. Kalachev and I. Asymptotic behavior of a solution of the Poisson equation in a model of a three-dimensional semiconductor structure.

Two-timing methods valid on expanding intervals. Approximate group analysis and multiple time scales method for the approximate Boussinesq equation. Nonlinear Dynam. Averaging for fundamental solutions of parabolic equations. Differential Equat 1 Bifurcation in classical bipolar transistor oscillator circuits. On the averaging method in nearly time-periodic advection-diffusion problems.

Kalachev and T. Kalachev and K. Global behavior and asymptotic reduction of a chemical kinetics system with continua of equilibria. Characterizing slow exit points. J Differential Equations, Kriegsmann and M. On the tracing of light rays through deformed glass rods with radially graded refractive indices. Matched Asymptotic Expansions: Ideas and Techniques.

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Lagerstrom and R. Basic concepts underlying singular perturbation techniques. Geometry and physics of averaging with applications. Two-variable expansions and singular perturbation problems. Shadowing lemma and singularly perturbed boundary value problems. Lynn and J. Uniform asymptotic solutions of second order linear ordinary differential equations with turning points.

Long and L. Asymptotic analysis of dissolution of a spherical bubble case of fast reaction outside the bubble. Rocky Mt. Lochak and C. Multiphase averaging for classical systems: with applications to adiabatic theorems. Lange and R. Singular perturbation analysis of boundary value problems for differential-difference equations.

### Asymptotic Analysis: A Distributional Approach

Small shifts with layer behaviour. Small shifts with rapid oscillations. Lu, A. MacGillivray, and S. Asymptotic behaviour of solutions of a similarity equation for laminar flows in channels with porous walls. Ima J. Luczak and J. Averaging over fast variables in the fluid limit for Markov chains: application to the supermarket model with memory. Annals Appl. Uniformly-valid asymptotic solutions to the Orr-Sommerfeld equation using multiple scales. Luongo and A. On the reconstitution problem in the multiple time-scale method. Lagerstrom and D. Note on logarithmic switchback terms in regular and singular perturbation expansions.

On a model equation of Lagerstrom. The existence of an overlap domain for a singular perturbation problem. On the switchback term in the asymptotic expansion of a model singular perturbation problem. De Maesschalck. Gevrey properties of real planar singularly perturbed systems. Extension of the WKB method to wave functions and transition probability amplitudes S-matrix for inelastic or reactive collisions.

Time-averaging under fast periodic forcing of parabolic partial differential equations: exponential estimates. The solutions of second order linear ordinary differential equations about a turning point of order two. Reduction of a model of an excitable cell to a one-dimensional map. On the approximation of double limits by single limits and the Kaplun extension theorem. Miller and R. Applied Asymptotic Analysis. The Korteweg-de Vries equation: a survey of results. Miura and M. MacGillivray, B. Liu, and N. Asymptotic analysis of the peeling-off point of a French duck. Methods Appl.

Mudavanhu and R. A new renormalization method for the asymptotic solution of weakly nonlinear vector systems. Existence and stability of periodic motion under higher order averaging. Differential Equat 64 1 Comparison of the modified method of averaging and the two variable expansion procedure. Amplitude expansions and normal forms in a model for thermohaline convection. Averaging of quasidifferential equations with fast and slow variables. Siberian Math. J 39 5 Moore and K. The semistrong limit of multipulse interaction in a thermally driven optical system.

Differential Equat 6 Meyer, J. Matkowsky and E. Singular perturbations of bifurcations. Mishchenko and N. Matthies and A. Exponential averaging for Hamiltonian evolution equations. Averaging theorems for conservative systems and the weakly compressible Euler equations. Some asymptotic estimates for higher order averaging and a comparison with iterated averaging.

Asymptotic Analysis. Perturbations: Theory and Methods. Murdock and L. Validity of the multiple scale method for very long intervals. Introduction to Perturbation Techniques. Resolving controversies in the application of the method of multiple scales and the generalized method of averaging. The separation of motions in systems with rapidly rotating phase. On averaging in two-frequency systems with small Hamiltonian and much smaller non-Hamiltonian perturbations.

Moscow Math. A modification of the boundary function method for singularly perturbed partial differential equations. Resonantly interacting waves. Nayfeh and D. Nonlinear Oscillations. Newman and D. Renormalization group analysis of the small-world network model. Two-scale renormalization-group classification of diffusive processes.

Oueini, C. Chin, and A. Dynamics of a cubic nonlinear vibration absorber. Nonlinear Dyn. Loss of boundary conditions in the asymptotic solution of linear ordinary differential equations, II boundary value problems. Examples illustrating the use of renormalization techniques for singularly perturbed differential equations. Two-timing and matched asymptotic expansions for singular perturbation problems. Ou and R. Shooting method for nonlinear singularly perturbed boundary-value problems. Deriving amplitude equations for weakly-nonlinear oscillators and their generalizations.

Higher order averaging and related methods for perturbed periodic and quasi-periodic systems. Hierarchies of iterated averages for systems of ordinary differential equations with a small parameter. Asymptotic stability and the method of iterated averages for almost periodic systems. Iterated averaging for periodic systems with hidden multi-scale slow times. Pacific J. Persek and F. Iterated averaging methods for systems of ordinary differential equations with a small parameter.

Painter and R. Turning-point connection at close quarters. Pontryagin and L. Approximate solution of a system of ordinary differential equations involving a small parameter in the derivatives. Papamikos and M. WKB approach applied to 1D time-dependent nonlinear Hamiltonian oscillators. Pavliotis and A. Multiscale Methods: Averaging and Homogenization. Pronin and D. Continuous averaging in multi-frequency slow-fast systems.

Chaotic Dyn. Percu, R. Temam, and D. Renormalization group method applied to the primitive equations. Pelinovsky and V. Averaging of dispersion-managed solitons: existence and stability. Gordon and Breach. Topics in Nonlinear Dynamics with Computer Algebra. Rinzel and B. Analysis of neural excitability and oscillations.

Koch and I. Segev eds. MIT Press. On multivariable asymptotic expansions. A new asymptotic method for jump phenomena. Rafei and W. Van Horssen. Solving systems of nonlinear difference equations by the multiple scales perturbation method. Sustained resonance for a nonlinear system with slowly varying coefficients.

Rosenblat and J. On the asymptotic solution of the Lagerstrom model equation. Ramis and R. Gevrey separation of fast and slow variables. The passage of weakly coupled nonlinear oscillators through internal resonance. On a derivative-expansion technique and some comments on multiple scaling in the asymptotic approximation of solutions of certain differential equations. Rubenfeld and B. Uniform asymptotic solutions for linear second order ordinary differential equations with turning points: formal theory. On the passage through resonance. Asymptotic approximations and extension of time-scales.

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