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August  2014, 34(8): i-iii. doi: 10.3934/dcds.2014.34.8i

Introduction

Adrian Constantin 1,

1. 

Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna

Published  January 2014

We survey the content of the present special issue devoted to nonlinear water waves.
Keywords: surface gravity waves, internal waves., Euler equations, free-boundary problem, Water waves.
Mathematics Subject Classification: Primary: 35Q31, 35Q35; Secondary: 76D3.
Citation: Adrian Constantin. Introduction. Discrete & Continuous Dynamical Systems - A, 2014, 34 (8) : i-iii. doi: 10.3934/dcds.2014.34.8i
References:
[1]

B. Buffoni and J. F. Toland, Analytic Theory of Global Bifurcation: An Introduction,, Princeton University Press, (2003).   Google Scholar

[2]

D. Clamond, New exact relations for easy recovery of steady wave profiles from bottom pressure measurements,, J. Fluid Mech., 726 (2013), 547.   Google Scholar

[3]

D. Clamond and A. Constantin, Recovery of steady periodic wave profiles from pressure measurements at the bed,, J. Fluid Mech., 714 (2013), 463.   Google Scholar

[4]

A. Constantin, Edge waves along a sloping beach,, J. Phys. A, 34 (2001), 9723.   Google Scholar

[5]

A. Constantin, The trajectories of particles in Stokes waves,, Invent. Math., 166 (2006), 523.   Google Scholar

[6]

A. Constantin, Particle trajectories in extreme Stokes waves,, IMA J. Appl. Math., 77 (2012), 293.   Google Scholar

[7]

A. Constantin, On the recovery of solitary wave profiles from pressure measurements,, J. Fluid Mech., 699 (2012), 376.   Google Scholar

[8]

A. Constantin, M. Ehrnström and E. Wahlén, Symmetry of steady periodic gravity water waves with vorticity,, Duke Math. J., 140 (2007), 591.   Google Scholar

[9]

A. Constantin and W. A. Strauss, Pressure beneath a Stokes wave,, Comm. Pure Appl. Math., 63 (2010), 533.   Google Scholar

[10]

E. Dancer, Bifurcation theory for analytic operators,, Proc. London Math. Soc., 26 (1973), 359.   Google Scholar

[11]

F. Gerstner, Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile,, Ann. Phys., 2 (1809), 412.   Google Scholar

[12]

D. Henry and R. Ivanov, One-dimensional weakly nonlinear model equations for Rossby waves,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3025.  doi: 10.3934/dcds.2014.34.3025.  Google Scholar

[13]

H.-C. Hsu, Recovering surface profiles of solitary waves on a uniform stream from pressure measurements,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3035.  doi: 10.3934/dcds.2014.34.3035.  Google Scholar

[14]

D. Ionescu-Kruse and A.-V. Matioc, Small-amplitude equatorial water waves with constant vorticity: Dispersion relations and particle trajectories,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3045.  doi: 10.3934/dcds.2014.34.3045.  Google Scholar

[15]

M. Kovalyov, On the nature of large and rogue waves,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3061.  doi: 10.3934/dcds.2014.34.3061.  Google Scholar

[16]

T. Lyons, Particle trajectories in extreme Stokes waves over infinite depth,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3095.  doi: 10.3934/dcds.2014.34.3095.  Google Scholar

[17]

C. I. Martin, Dispersion relations for periodic water waves with surface tension and discontinuous vorticity,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3109.  doi: 10.3934/dcds.2014.34.3109.  Google Scholar

[18]

B.-V. Matioc, A characterization of the symmetric steady water waves in terms of the underlying flow,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3125.  doi: 10.3934/dcds.2014.34.3125.  Google Scholar

[19]

A. Nachbin and R. Ribeiro-Junior, A boundary integral formulation for particle trajectories in Stokes waves,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3135.  doi: 10.3934/dcds.2014.34.3135.  Google Scholar

[20]

H. Okamoto, T. Sakajo and M. Wunsch, Steady-states and traveling-wave solutions of the generalized Constantin-Lax-Majda equation,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3155.  doi: 10.3934/dcds.2014.34.3155.  Google Scholar

[21]

K. Oliveras, V. Vasan, B. Deconinck and D. Henderson, Recovering the water-wave profile from pressure measurements,, SIAM J. Appl. Math., 72 (2012), 897.   Google Scholar

[22]

P. Rabinowitz, Some global results for nonlinear eigenvalue problems,, J. Funct. Anal., 7 (1971), 487.   Google Scholar

[23]

M. Stiassnie and R. Stuhlmeier, Progressive waves on a blunt interface,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3171.  doi: 10.3934/dcds.2014.34.3171.  Google Scholar

[24]

R. Stuhlmeier, Internal Gerstner waves on a sloping bed,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3183.  doi: 10.3934/dcds.2014.34.3183.  Google Scholar

[25]

J. F. Toland, Energy-minimising parallel flows with prescribed vorticity distribution,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3193.  doi: 10.3934/dcds.2014.34.3193.  Google Scholar

[26]

J. F. Toland, Non-existence of global energy minimisers in Stokes waves problems,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3211.  doi: 10.3934/dcds.2014.34.3211.  Google Scholar

[27]

V. Vasan and K. Oliveras, Pressure beneath a traveling wave with constant vorticity,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3219.  doi: 10.3934/dcds.2014.34.3219.  Google Scholar

[28]

S. Walsh, Steady stratified periodic gravity waves with surface tension: Local bifurcation,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3241.  doi: 10.3934/dcds.2014.34.3241.  Google Scholar

[29]

S. Walsh, Steady stratified periodic gravity waves with surface tension: Global bifurcation,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3287.  doi: 10.3934/dcds.2014.34.3287.  Google Scholar

show all references

References:
[1]

B. Buffoni and J. F. Toland, Analytic Theory of Global Bifurcation: An Introduction,, Princeton University Press, (2003).   Google Scholar

[2]

D. Clamond, New exact relations for easy recovery of steady wave profiles from bottom pressure measurements,, J. Fluid Mech., 726 (2013), 547.   Google Scholar

[3]

D. Clamond and A. Constantin, Recovery of steady periodic wave profiles from pressure measurements at the bed,, J. Fluid Mech., 714 (2013), 463.   Google Scholar

[4]

A. Constantin, Edge waves along a sloping beach,, J. Phys. A, 34 (2001), 9723.   Google Scholar

[5]

A. Constantin, The trajectories of particles in Stokes waves,, Invent. Math., 166 (2006), 523.   Google Scholar

[6]

A. Constantin, Particle trajectories in extreme Stokes waves,, IMA J. Appl. Math., 77 (2012), 293.   Google Scholar

[7]

A. Constantin, On the recovery of solitary wave profiles from pressure measurements,, J. Fluid Mech., 699 (2012), 376.   Google Scholar

[8]

A. Constantin, M. Ehrnström and E. Wahlén, Symmetry of steady periodic gravity water waves with vorticity,, Duke Math. J., 140 (2007), 591.   Google Scholar

[9]

A. Constantin and W. A. Strauss, Pressure beneath a Stokes wave,, Comm. Pure Appl. Math., 63 (2010), 533.   Google Scholar

[10]

E. Dancer, Bifurcation theory for analytic operators,, Proc. London Math. Soc., 26 (1973), 359.   Google Scholar

[11]

F. Gerstner, Theorie der Wellen samt einer daraus abgeleiteten Theorie der Deichprofile,, Ann. Phys., 2 (1809), 412.   Google Scholar

[12]

D. Henry and R. Ivanov, One-dimensional weakly nonlinear model equations for Rossby waves,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3025.  doi: 10.3934/dcds.2014.34.3025.  Google Scholar

[13]

H.-C. Hsu, Recovering surface profiles of solitary waves on a uniform stream from pressure measurements,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3035.  doi: 10.3934/dcds.2014.34.3035.  Google Scholar

[14]

D. Ionescu-Kruse and A.-V. Matioc, Small-amplitude equatorial water waves with constant vorticity: Dispersion relations and particle trajectories,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3045.  doi: 10.3934/dcds.2014.34.3045.  Google Scholar

[15]

M. Kovalyov, On the nature of large and rogue waves,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3061.  doi: 10.3934/dcds.2014.34.3061.  Google Scholar

[16]

T. Lyons, Particle trajectories in extreme Stokes waves over infinite depth,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3095.  doi: 10.3934/dcds.2014.34.3095.  Google Scholar

[17]

C. I. Martin, Dispersion relations for periodic water waves with surface tension and discontinuous vorticity,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3109.  doi: 10.3934/dcds.2014.34.3109.  Google Scholar

[18]

B.-V. Matioc, A characterization of the symmetric steady water waves in terms of the underlying flow,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3125.  doi: 10.3934/dcds.2014.34.3125.  Google Scholar

[19]

A. Nachbin and R. Ribeiro-Junior, A boundary integral formulation for particle trajectories in Stokes waves,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3135.  doi: 10.3934/dcds.2014.34.3135.  Google Scholar

[20]

H. Okamoto, T. Sakajo and M. Wunsch, Steady-states and traveling-wave solutions of the generalized Constantin-Lax-Majda equation,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3155.  doi: 10.3934/dcds.2014.34.3155.  Google Scholar

[21]

K. Oliveras, V. Vasan, B. Deconinck and D. Henderson, Recovering the water-wave profile from pressure measurements,, SIAM J. Appl. Math., 72 (2012), 897.   Google Scholar

[22]

P. Rabinowitz, Some global results for nonlinear eigenvalue problems,, J. Funct. Anal., 7 (1971), 487.   Google Scholar

[23]

M. Stiassnie and R. Stuhlmeier, Progressive waves on a blunt interface,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3171.  doi: 10.3934/dcds.2014.34.3171.  Google Scholar

[24]

R. Stuhlmeier, Internal Gerstner waves on a sloping bed,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3183.  doi: 10.3934/dcds.2014.34.3183.  Google Scholar

[25]

J. F. Toland, Energy-minimising parallel flows with prescribed vorticity distribution,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3193.  doi: 10.3934/dcds.2014.34.3193.  Google Scholar

[26]

J. F. Toland, Non-existence of global energy minimisers in Stokes waves problems,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3211.  doi: 10.3934/dcds.2014.34.3211.  Google Scholar

[27]

V. Vasan and K. Oliveras, Pressure beneath a traveling wave with constant vorticity,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3219.  doi: 10.3934/dcds.2014.34.3219.  Google Scholar

[28]

S. Walsh, Steady stratified periodic gravity waves with surface tension: Local bifurcation,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3241.  doi: 10.3934/dcds.2014.34.3241.  Google Scholar

[29]

S. Walsh, Steady stratified periodic gravity waves with surface tension: Global bifurcation,, Discr. Cont. Dyn. Syst. A, 34 (2014), 3287.  doi: 10.3934/dcds.2014.34.3287.  Google Scholar

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