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New evolution equations for nonlinear water waves in general bathymetry with application to steady travelling solutions in constant, but arbitrary, depth
1.  School of Naval Architecture & Marine Engineering, National Technical University of Athens, Heroon Polytechniou 9, Athens 15773, Greece 
2.  School of Technological Applications, Technological Educational Institute of Athens, Greece 
[1] 
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R. S. Johnson. A selection of nonlinear problems in water waves, analysed by perturbationparameter techniques. Communications on Pure & Applied Analysis, 2012, 11 (4) : 14971522. doi: 10.3934/cpaa.2012.11.1497 
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Dan Endres, Martin Kummer. Nonlinear normal modes for the isosceles DST. Conference Publications, 1998, 1998 (Special) : 231241. doi: 10.3934/proc.1998.1998.231 
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Santosh Bhattarai. Stability of normalized solitary waves for three coupled nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems  A, 2016, 36 (4) : 17891811. doi: 10.3934/dcds.2016.36.1789 
[5] 
Robert McOwen, Peter Topalov. Asymptotics in shallow water waves. Discrete & Continuous Dynamical Systems  A, 2015, 35 (7) : 31033131. doi: 10.3934/dcds.2015.35.3103 
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Calin Iulian Martin. A Hamiltonian approach for nonlinear rotational capillarygravity water waves in stratified flows. Discrete & Continuous Dynamical Systems  A, 2017, 37 (1) : 387404. doi: 10.3934/dcds.2017016 
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Walter A. Strauss. Vorticity jumps in steady water waves. Discrete & Continuous Dynamical Systems  B, 2012, 17 (4) : 11011112. doi: 10.3934/dcdsb.2012.17.1101 
[8] 
Vera Mikyoung Hur. On the formation of singularities for surface water waves. Communications on Pure & Applied Analysis, 2012, 11 (4) : 14651474. doi: 10.3934/cpaa.2012.11.1465 
[9] 
Jerry L. Bona, Henrik Kalisch. Models for internal waves in deep water. Discrete & Continuous Dynamical Systems  A, 2000, 6 (1) : 120. doi: 10.3934/dcds.2000.6.1 
[10] 
Martina ChirilusBruckner, Guido Schneider. Interaction of oscillatory packets of water waves. Conference Publications, 2015, 2015 (special) : 267275. doi: 10.3934/proc.2015.0267 
[11] 
Jonathan J. Wylie, Robert M. Miura, Huaxiong Huang. Systems of coupled diffusion equations with degenerate nonlinear source terms: Linear stability and traveling waves. Discrete & Continuous Dynamical Systems  A, 2009, 23 (1&2) : 561569. doi: 10.3934/dcds.2009.23.561 
[12] 
Nghiem V. Nguyen, ZhiQiang Wang. Existence and stability of a twoparameter family of solitary waves for a 2coupled nonlinear Schrödinger system. Discrete & Continuous Dynamical Systems  A, 2016, 36 (2) : 10051021. doi: 10.3934/dcds.2016.36.1005 
[13] 
Tetsu Mizumachi, Dmitry Pelinovsky. On the asymptotic stability of localized modes in the discrete nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems  S, 2012, 5 (5) : 971987. doi: 10.3934/dcdss.2012.5.971 
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Vincent Duchêne, Samer Israwi, Raafat Talhouk. Shallow water asymptotic models for the propagation of internal waves. Discrete & Continuous Dynamical Systems  S, 2014, 7 (2) : 239269. doi: 10.3934/dcdss.2014.7.239 
[15] 
AncaVoichita Matioc. On particle trajectories in linear deepwater waves. Communications on Pure & Applied Analysis, 2012, 11 (4) : 15371547. doi: 10.3934/cpaa.2012.11.1537 
[16] 
Jerry L. Bona, Thierry Colin, Colette Guillopé. Propagation of longcrested water waves. Discrete & Continuous Dynamical Systems  A, 2013, 33 (2) : 599628. doi: 10.3934/dcds.2013.33.599 
[17] 
Angel Castro, Diego Córdoba, Charles Fefferman, Francisco Gancedo, Javier GómezSerrano. Structural stability for the splash singularities of the water waves problem. Discrete & Continuous Dynamical Systems  A, 2014, 34 (12) : 49975043. doi: 10.3934/dcds.2014.34.4997 
[18] 
Mats Ehrnström, Gabriele Villari. Recent progress on particle trajectories in steady water waves. Discrete & Continuous Dynamical Systems  B, 2009, 12 (3) : 539559. doi: 10.3934/dcdsb.2009.12.539 
[19] 
David M. Ambrose, Jerry L. Bona, David P. Nicholls. Wellposedness of a model for water waves with viscosity. Discrete & Continuous Dynamical Systems  B, 2012, 17 (4) : 11131137. doi: 10.3934/dcdsb.2012.17.1113 
[20] 
David Henry, BogdanVasile Matioc. On the regularity of steady periodic stratified water waves. Communications on Pure & Applied Analysis, 2012, 11 (4) : 14531464. doi: 10.3934/cpaa.2012.11.1453 
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