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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 
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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 
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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 
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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 
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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 
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Martina ChirilusBruckner, Guido Schneider. Interaction of oscillatory packets of water waves. Conference Publications, 2015, 2015 (special) : 267275. doi: 10.3934/proc.2015.0267 
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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 
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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 
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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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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 
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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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Gerhard Tulzer. On the symmetry of steady periodic water waves with stagnation points. Communications on Pure & Applied Analysis, 2012, 11 (4) : 15771586. doi: 10.3934/cpaa.2012.11.1577 
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David Henry, HungChu Hsu. Instability of equatorial water waves in the $f$plane. Discrete & Continuous Dynamical Systems  A, 2015, 35 (3) : 909916. doi: 10.3934/dcds.2015.35.909 
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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 
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