# zbMATH — the first resource for mathematics

## Eckhaus, Wiktor

Compute Distance To:
 Author ID: eckhaus.wiktor Published as: Eckhaus, W.; Eckhaus, Wiktor External Links: MGP · Wikidata · GND
 Documents Indexed: 53 Publications since 1961, including 9 Books Biographic References: 1 Publication
all top 5

#### Co-Authors

 22 single-authored 7 van Harten, Aart 6 Doelman, Arjen 4 Garbey, Marc 3 Brauner, Claude-Michel 3 Calogero, Francesco A. 3 de Jager, Eduard M. 3 Kaper, Tasso J. 3 Peradzyński, Zbigniew 2 Kuske, Rachel A. 1 Besseling, J. F. 1 Cook, L. Pamela 1 DiPrima, Richard C. 1 Duistermaat, Johannes Jisse 1 Iooss, Gérard 1 Moet, Henry Johan Karel 1 Penning, H. P. 1 Schielen, Ralph 1 Schuur, Peter Cornelis 1 Segel, Lee Aaron 1 Trad, A. T. 1 van der Wel, F. V. 1 Verhulst, Ferdinand
all top 5

#### Serials

 4 SIAM Journal on Applied Mathematics 4 North-Holland Mathematics Studies 3 Inverse Problems 3 Physica D 3 SIAM Journal on Mathematical Analysis 3 SIAM Review 2 Journal of Fluid Mechanics 1 Archives of Mechanics 1 Archive for Rational Mechanics and Analysis 1 International Journal of Non-Linear Mechanics 1 Journal of Mathematical Analysis and Applications 1 Mathematical Methods in the Applied Sciences 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Verslag van de Gewone Vergadering van de Afdeling Natuurkunde 1 Studies in Applied Mathematics 1 European Journal of Mechanics. B. Fluids 1 Bulletin de l’Académie Polonaise des Sciences, Série des Sciences Techniques 1 Nieuw Archief voor Wiskunde. Derde Serie 1 Journal of Nonlinear Science 1 Journal of the Aerospace Sciences 1 Journal de Mécanique 1 Epsilon Uitgaven 1 Lecture Notes in Mathematics
all top 5

#### Fields

 30 Partial differential equations (35-XX) 20 Ordinary differential equations (34-XX) 13 Fluid mechanics (76-XX) 4 General and overarching topics; collections (00-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Mechanics of particles and systems (70-XX) 3 Biology and other natural sciences (92-XX) 2 Approximations and expansions (41-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Numerical analysis (65-XX) 1 Mechanics of deformable solids (74-XX) 1 Geophysics (86-XX)

#### Citations contained in zbMATH Open

37 Publications have been cited 802 times in 676 Documents Cited by Year
Studies in non-linear stability theory. Zbl 0125.33101
Eckhaus, W.
1965
Asymptotic analysis of singular perturbations. Zbl 0421.34057
Eckhaus, Wiktor
1979
Relaxation oscillations including a standard chase on French ducks. Zbl 0509.34037
Eckhaus, Wiktor
1983
Matched asymptotic expansions and singular perturbations. Zbl 0255.34002
Eckhaus, Wiktor
1973
Nonlinear evolution equations, rescalings, model PDEs and their integrability. I. Zbl 0645.35087
Calogero, Francesco; Eckhaus, Wiktor
1987
Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type. Zbl 0151.15101
Eckhaus, W.; de Jager, E. M.
1966
Boundary layers in linear elliptic singular perturbation problems. Zbl 0234.35009
Eckhaus, Wiktor
1972
Non-linear wave-number interaction in near-critical two-dimensional flows. Zbl 0229.76039
Diprima, R. C.; Eckhaus, W.; Segel, L. A.
1971
The inverse scattering transformation and the theory of solitons. An introduction. Zbl 0463.35001
Eckhaus, Wiktor; van Harten, Aart
1981
Periodic and quasi-periodic solutions of degenerate modulation equations. Zbl 0744.35058
Doelman, Arjen; Eckhaus, Wiktor
1991
Slowly modulated two-pulse solutions in the Gray-Scott model. I: Asymptotic construction and stability. Zbl 0979.35074
Doelman, Arjen; Eckhaus, Wiktor; Kaper, Tasso J.
2000
Slowly modulated two-pulse solutions in the Gray–Scott model. II: Geometric theory, bifurcations, and splitting dynamics. Zbl 0989.35073
Doelman, Arjen; Eckhaus, Wiktor; Kaper, Tasso J.
2001
Strong selection or rejection of spatially periodic patterns in degenerate bifurcations. Zbl 0677.76046
Eckhaus, Wiktor; Iooss, Gérard
1989
The emergence of solitons of the Korteweg-de Vries equation from arbitrary initial conditions. Zbl 0518.35074
Eckhaus, W.; Schuur, P.
1983
The Ginzburg-Landau manifold is an attractor. Zbl 0797.35070
Eckhaus, W.
1993
Nonlinear evolution equations, rescalings, model PDEs and their integrability. II. Zbl 0702.35210
Calogero, Francesco; Eckhaus, Wiktor
1988
Resonance in a boundary value problem of singular perturbation type. Zbl 0264.34070
Cook, L. Pamela; Eckhaus, W.
1973
Singular perturbations of homoclinic orbits in $${\mathbb{R}{}}^ 4$$. Zbl 0760.34048
Eckhaus, Wiktor
1992
New approach to the asymptotic theory of nonlinear oscillations and wave- propagation. Zbl 0296.34038
Eckhaus, Wiktor
1975
Fundamental concepts of matching. Zbl 0806.35015
Eckhaus, Wiktor
1994
Formal approximations and singular perturbations. Zbl 0384.35007
Eckhaus, Wiktor
1977
Theory of flame-front stability. Zbl 0098.41801
Eckhaus, Wiktor
1961
Asymptotic analysis on large timescales for singular perturbations of hyperbolic type. Zbl 0703.65054
Eckhaus, W.; Garbey, M.
1990
The long-time behaviour for perturbed wave-equations and related problems. Zbl 0629.35085
Eckhaus, Wiktor
1986
A singularly perturbed free boundary problem describing a laser sustained plasma. Zbl 0566.35060
Eckhaus, Wiktor; Van Harten, Aart; Peradzynski, Zbigniew
1985
Theory and applications of singular perturbations. Proceedings of a Conference Held in Oberwolfach, August 16-22, 1981. Zbl 0478.00011
Eckhaus, W. (ed.); de Jager, E. M. (ed.)
1982
Matching principles and composite expansions. Zbl 0374.35007
Eckhaus, Wiktor
1977
Two-body problem with slowly decreasing mass. Zbl 0217.54503
Verhulst, F.; Eckhaus, W.
1970
On water waves at Froude number slightly higher than one and Bond number less than 1/3. Zbl 0764.76008
Eckhaus, Wiktor
1992
Necessary conditions for integrability of nonlinear PDEs. Zbl 0645.35089
Calogero, Francesco; Eckhaus, Wiktor
1987
Asymptotic solutions in free boundary problems of singularly perturbed elliptic variational inequalities. Zbl 0395.35004
Eckhaus, W.; Moet, H. J. K.
1978
Pattern formation in systems with slowly varying geometry. Zbl 0870.35051
Eckhaus, Wiktor; Kuske, Rachel
1997
Analysis of ordinary differential equations. Zbl 1342.34002
Duistermaat, Johannes Jisse; Eckhaus, Wiktor
1995
The theory of ducks. Zbl 0785.34038
Eckhaus, W.
1993
Plasma produced by a laser in a medium with convection and free surface satisfying a Hamilton-Jacobi equation. Zbl 0654.76116
Eckhaus, W.; Van Harten, A.; Peradzyński, Z.
1987
On some basic concepts in the analysis of singular perturbations. Zbl 0492.34047
Eckhaus, Wiktor
1980
Sur l’influence de l’epaisseur dans le problème de diffraction de Sommerfeld. Zbl 0151.43101
1966
Slowly modulated two-pulse solutions in the Gray–Scott model. II: Geometric theory, bifurcations, and splitting dynamics. Zbl 0989.35073
Doelman, Arjen; Eckhaus, Wiktor; Kaper, Tasso J.
2001
Slowly modulated two-pulse solutions in the Gray-Scott model. I: Asymptotic construction and stability. Zbl 0979.35074
Doelman, Arjen; Eckhaus, Wiktor; Kaper, Tasso J.
2000
Pattern formation in systems with slowly varying geometry. Zbl 0870.35051
Eckhaus, Wiktor; Kuske, Rachel
1997
Analysis of ordinary differential equations. Zbl 1342.34002
Duistermaat, Johannes Jisse; Eckhaus, Wiktor
1995
Fundamental concepts of matching. Zbl 0806.35015
Eckhaus, Wiktor
1994
The Ginzburg-Landau manifold is an attractor. Zbl 0797.35070
Eckhaus, W.
1993
The theory of ducks. Zbl 0785.34038
Eckhaus, W.
1993
Singular perturbations of homoclinic orbits in $${\mathbb{R}{}}^ 4$$. Zbl 0760.34048
Eckhaus, Wiktor
1992
On water waves at Froude number slightly higher than one and Bond number less than 1/3. Zbl 0764.76008
Eckhaus, Wiktor
1992
Periodic and quasi-periodic solutions of degenerate modulation equations. Zbl 0744.35058
Doelman, Arjen; Eckhaus, Wiktor
1991
Asymptotic analysis on large timescales for singular perturbations of hyperbolic type. Zbl 0703.65054
Eckhaus, W.; Garbey, M.
1990
Strong selection or rejection of spatially periodic patterns in degenerate bifurcations. Zbl 0677.76046
Eckhaus, Wiktor; Iooss, Gérard
1989
Nonlinear evolution equations, rescalings, model PDEs and their integrability. II. Zbl 0702.35210
Calogero, Francesco; Eckhaus, Wiktor
1988
Nonlinear evolution equations, rescalings, model PDEs and their integrability. I. Zbl 0645.35087
Calogero, Francesco; Eckhaus, Wiktor
1987
Necessary conditions for integrability of nonlinear PDEs. Zbl 0645.35089
Calogero, Francesco; Eckhaus, Wiktor
1987
Plasma produced by a laser in a medium with convection and free surface satisfying a Hamilton-Jacobi equation. Zbl 0654.76116
Eckhaus, W.; Van Harten, A.; Peradzyński, Z.
1987
The long-time behaviour for perturbed wave-equations and related problems. Zbl 0629.35085
Eckhaus, Wiktor
1986
A singularly perturbed free boundary problem describing a laser sustained plasma. Zbl 0566.35060
Eckhaus, Wiktor; Van Harten, Aart; Peradzynski, Zbigniew
1985
Relaxation oscillations including a standard chase on French ducks. Zbl 0509.34037
Eckhaus, Wiktor
1983
The emergence of solitons of the Korteweg-de Vries equation from arbitrary initial conditions. Zbl 0518.35074
Eckhaus, W.; Schuur, P.
1983
Theory and applications of singular perturbations. Proceedings of a Conference Held in Oberwolfach, August 16-22, 1981. Zbl 0478.00011
Eckhaus, W. (ed.); de Jager, E. M. (ed.)
1982
The inverse scattering transformation and the theory of solitons. An introduction. Zbl 0463.35001
Eckhaus, Wiktor; van Harten, Aart
1981
On some basic concepts in the analysis of singular perturbations. Zbl 0492.34047
Eckhaus, Wiktor
1980
Asymptotic analysis of singular perturbations. Zbl 0421.34057
Eckhaus, Wiktor
1979
Asymptotic solutions in free boundary problems of singularly perturbed elliptic variational inequalities. Zbl 0395.35004
Eckhaus, W.; Moet, H. J. K.
1978
Formal approximations and singular perturbations. Zbl 0384.35007
Eckhaus, Wiktor
1977
Matching principles and composite expansions. Zbl 0374.35007
Eckhaus, Wiktor
1977
New approach to the asymptotic theory of nonlinear oscillations and wave- propagation. Zbl 0296.34038
Eckhaus, Wiktor
1975
Matched asymptotic expansions and singular perturbations. Zbl 0255.34002
Eckhaus, Wiktor
1973
Resonance in a boundary value problem of singular perturbation type. Zbl 0264.34070
Cook, L. Pamela; Eckhaus, W.
1973
Boundary layers in linear elliptic singular perturbation problems. Zbl 0234.35009
Eckhaus, Wiktor
1972
Non-linear wave-number interaction in near-critical two-dimensional flows. Zbl 0229.76039
Diprima, R. C.; Eckhaus, W.; Segel, L. A.
1971
Two-body problem with slowly decreasing mass. Zbl 0217.54503
Verhulst, F.; Eckhaus, W.
1970
Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type. Zbl 0151.15101
Eckhaus, W.; de Jager, E. M.
1966
Sur l’influence de l’epaisseur dans le problème de diffraction de Sommerfeld. Zbl 0151.43101
1966
Studies in non-linear stability theory. Zbl 0125.33101
Eckhaus, W.
1965
Theory of flame-front stability. Zbl 0098.41801
Eckhaus, Wiktor
1961
all top 5

#### Cited by 906 Authors

 19 Doelman, Arjen 18 Schneider, Guido 17 Temam, Roger Meyer 16 Jung, Changyeol 15 Kadalbajoo, Mohan K. 9 Kaper, Tasso J. 9 Maccari, Attilio 8 Howes, Fred A. 8 Reddy, Yanala Narsimha 7 Desroches, Mathieu 7 Krupa, Martin 7 Mancas, Stefan C. 7 Shen, Huichuan 7 Szmolyan, Peter 7 Ward, Michael J. 6 Eckhaus, Wiktor 6 Knobloch, Edgar 6 Kolokolnikov, Theodore 6 Kramer, Lorenz 6 Malomed, Boris A. 6 Martel, Yvan 6 Merle, Frank 6 van Harten, Aart 6 Wei, Juncheng 5 Bridges, Thomas J. 5 Calogero, Francesco A. 5 Hong, Youngjoon 5 Nunez, Manuel A. 5 Wechselberger, Martin 4 De Maesschalck, Peter 4 Fruchard, Augustin 4 Gie, Gung-Min 4 Hamouda, Makram 4 Han, Maoan 4 Kuske, Rachel A. 4 Levi, Decio 4 Mielke, Alexander 4 Patidar, Kailash C. 4 Rademacher, Jens Diederich Michael 4 Roychoudhury, Satrajit 4 Verhulst, Ferdinand 4 Zumbrun, Kevin R. 3 Banasiak, Jacek 3 Bastiaansen, Robbin 3 Bodenschatz, Eberhard 3 Choudhury, Sumitra Roy 3 de Groen, Pieter P. N. 3 de Mottoni, Piero 3 Duan, Jinqiao 3 Düll, Wolf-Patrick 3 Duyckaerts, Thomas 3 Grasman, Johan 3 Imaikin, Valery 3 Kapitula, Todd M. 3 Kaushik, Aditya 3 Kenig, Carlos Eduardo 3 Komech, Alexander Ilich 3 Kühn, Christian 3 Lin, Ming-Che 3 Lin, Xiaobiao 3 Matkowsky, Bernard J. 3 Nishiura, Yasumasa 3 Qiu, Deqin 3 Rotstein, Horacio G. 3 Rottschäfer, Vivi 3 Sanchez-Palencia, Enrique 3 Schäfke, Reinhard 3 Sengupta, Tapan K. 3 Tordeux, Sébastien 3 Tursunov, Dilmurat Abdillazhanovich 3 Tzou, J. C. 3 Wang, Xiaoming 3 Zimmermann, Dominik 2 Ai, Shangbing 2 Algaba, Antonio 2 Aranson, Igor S. 2 Arora, Puneet 2 Barker, Blake 2 Bendali, Abderrahmane 2 Berg, Lothar 2 Besjes, J. G. 2 Bobisud, Larry E. 2 Bockelman, Brian 2 Braaksma, Barteld 2 Brauner, Claude-Michel 2 Budd, Christopher John 2 Burke, John L. 2 Carter, Paul M. 2 Chen, Cha’o-Kuang 2 Cheng, Wenguang 2 Chiffaudel, Arnaud 2 Chirilus-Bruckner, Martina 2 Chung, Kwok-Wai 2 Clavin, Paul 2 Cong, Hongzi 2 Côte, Raphaël 2 Coulaud, Olivier 2 Daripa, Prabir K. 2 Dash, Ranjan K. 2 Daviaud, François ...and 806 more Authors
all top 5

#### Cited in 176 Serials

 76 Physica D 30 Journal of Mathematical Physics 28 Journal of Differential Equations 26 Journal of Mathematical Analysis and Applications 18 Applied Mathematics and Computation 17 Journal of Nonlinear Science 15 Chaos 11 Archive for Rational Mechanics and Analysis 11 Computers & Mathematics with Applications 11 Journal of Fluid Mechanics 11 ZAMP. Zeitschrift für angewandte Mathematik und Physik 11 Studies in Applied Mathematics 11 Applied Mathematics and Mechanics. (English Edition) 11 Applied Mathematics Letters 9 Mathematical Methods in the Applied Sciences 9 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 8 Communications in Mathematical Physics 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Communications in Partial Differential Equations 8 Journal of Dynamics and Differential Equations 7 Chaos, Solitons and Fractals 7 Nonlinear Analysis. Theory, Methods & Applications 6 Journal of Engineering Mathematics 6 Journal of Mathematical Biology 6 Physics Letters. A 6 Journal of Computational and Applied Mathematics 6 Transactions of the American Mathematical Society 6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 6 Nonlinear Dynamics 5 International Journal of Engineering Science 5 Mathematics and Computers in Simulation 5 RAIRO. Modélisation Mathématique et Analyse Numérique 5 Mathematical and Computer Modelling 5 Celestial Mechanics 5 Discrete and Continuous Dynamical Systems 5 SIAM Journal on Applied Dynamical Systems 4 Applicable Analysis 4 Computer Methods in Applied Mechanics and Engineering 4 Fluid Dynamics 4 Journal of Computational Physics 4 Journal of Statistical Physics 4 Physica A 4 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Acta Applicandae Mathematicae 4 Numerical Methods for Partial Differential Equations 4 European Journal of Applied Mathematics 4 Communications in Nonlinear Science and Numerical Simulation 4 Journal of Nonlinear Mathematical Physics 4 Nonlinear Analysis. Real World Applications 3 Computers and Fluids 3 Journal of Applied Mathematics and Mechanics 3 Mathematical Biosciences 3 Nonlinearity 3 Physics of Fluids 3 Theoretical and Mathematical Physics 3 Wave Motion 3 Mathematics of Computation 3 Theoretical and Computational Fluid Dynamics 3 Automatica 3 Journal of Optimization Theory and Applications 3 Numerische Mathematik 3 Applied Numerical Mathematics 3 Journal of Scientific Computing 3 Japan Journal of Industrial and Applied Mathematics 3 International Journal of Computer Mathematics 3 SIAM Journal on Mathematical Analysis 3 Dynamical Systems 2 International Journal of Modern Physics B 2 Communications on Pure and Applied Mathematics 2 Journal d’Analyse Mathématique 2 Rocky Mountain Journal of Mathematics 2 Inventiones Mathematicae 2 Journal of Functional Analysis 2 Mathematische Nachrichten 2 Mathematische Zeitschrift 2 Meccanica 2 Numerical Functional Analysis and Optimization 2 Chinese Annals of Mathematics. Series B 2 Communications in Applied Numerical Methods 2 Applications of Mathematics 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Geometric and Functional Analysis. GAFA 2 Applied Mathematical Modelling 2 SIAM Journal on Applied Mathematics 2 Physics of Fluids 2 Abstract and Applied Analysis 2 Mathematical Physics, Analysis and Geometry 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 European Journal of Mechanics. B. Fluids 2 Lobachevskii Journal of Mathematics 2 Analysis and Applications (Singapore) 2 Séminaire Laurent Schwartz. EDP et Applications 2 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Biological Cybernetics 1 International Journal of Solids and Structures 1 Israel Journal of Mathematics 1 Physics Reports 1 Reviews of Modern Physics 1 Russian Mathematical Surveys ...and 76 more Serials
all top 5

#### Cited in 36 Fields

 377 Partial differential equations (35-XX) 157 Ordinary differential equations (34-XX) 152 Fluid mechanics (76-XX) 126 Dynamical systems and ergodic theory (37-XX) 85 Numerical analysis (65-XX) 59 Biology and other natural sciences (92-XX) 31 Mechanics of deformable solids (74-XX) 21 Mechanics of particles and systems (70-XX) 20 Classical thermodynamics, heat transfer (80-XX) 18 Optics, electromagnetic theory (78-XX) 18 Statistical mechanics, structure of matter (82-XX) 12 Quantum theory (81-XX) 11 Systems theory; control (93-XX) 10 Approximations and expansions (41-XX) 10 Probability theory and stochastic processes (60-XX) 8 Global analysis, analysis on manifolds (58-XX) 8 Geophysics (86-XX) 7 Operator theory (47-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 6 Difference and functional equations (39-XX) 3 Nonassociative rings and algebras (17-XX) 3 Integral transforms, operational calculus (44-XX) 3 Statistics (62-XX) 3 Computer science (68-XX) 3 Relativity and gravitational theory (83-XX) 2 History and biography (01-XX) 2 Real functions (26-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 Differential geometry (53-XX) 1 Algebraic geometry (14-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)

#### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.