Communications on Pure and Applied Analysis (CPAA)

On the existence and computation of periodic travelling waves for a 2D water wave model
Pages: 557 - 578, Issue 2, March 2018

doi:doi:10.3934/cpaa.2018030      Abstract        References        Full text (716.7K)           Related Articles

José Raúl Quintero - Departamento de Matemáticas, Universidad del Valle, Calle 13 Nro. 100-00, Cali, Colombia (email)
Juan Carlos Muñoz Grajales - Departamento de Matemáticas, Universidad del Valle, Calle 13 Nro. 100-00, Cali, Colombia (email)

1 U. M. Asher, S. J. Ruuth and B. T. R. Wetton, Implicit-explicit methods for time-dependent partial differential equations, SIAM J. Numer. Anal., 32 (1995), 797-823.       
2 C. Canuto, M. Y. Hussaini and A. Quarteroni, Spectral Methods in Fluid Dynamics, Series in Computational Physics, 1988, Springer, Berlin.       
3 G. E. Karniadakis, M. Israeli and S. A. Orszag, High-order splitting methods for the incompressible Navier-Stokes equations, J. Comput. Phys., 97 (1991), 414-443.       
4 T. Kato, Quasilinear equations of evolution with applications to partial differential equations, Proceedings of the symposium at Dundee, Lecture Notes in Mathematics, 448, Springer, (1975), 25-70.       
5 T. Kato, On the Korteweg-de Vries equation, Manuscripta Mathematica, 28 (1979), 89-99.       
6 T. Kato, On the Cauchy problem for the (generalized) Korteweg-de Vries equation, Studies in Applied Mathematics, Advances in Mathematics, Supplementary Studies, 8, Academic Press, (1983), 92-128.       
7 J. Kim and P. Moin, Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys., 59 (1985), 308-323.       
8 K. R. Meyer, G. R. Hall and D. Offin, Introduction to Hamiltonian Dynamical Systems and the N-Body problem, 2nd ed. Applied Mathematical Sciences, vol. 90, 2009, Springer-Verlag.       
9 P. A. Milewski and J. B. Keller, Three dimensional water waves, Studies Appl. Math., 37 (1996), 149-166.       
10 L. Paumond, A rigorous link between KP and a Benney-Luke Equation, Diff. Int. Eq., 16 (2003), 1039-1064.       
11 J. Quintero, Solitary water waves for a 2D Boussinesq type system, J. Part. Diff. Eqs., 23 (2010), 251-280.       
12 J. Quintero, The Cauchy problem and stability of solitary waves for a 2D Boussinesq-KdV type system, Diff. Int. Eqs., 21 (2011), 325-360.       
13 J. Quintero, From periodic travelling waves to solitons of a 2D water wave system, Meth. Appl. Anal., 21 (2014), 241-264.       
14 J. Quintero, A water wave mixed type problem: existence of periodic travelling waves for a 2D Boussinesq system, Rev. Academia Colombiana de Ciencias Naturales, Físicas y Exactas., 38 (2015), 6-17.       
15 J. R. Quintero and R. L. Pego, Two-dimensional solitary waves for a Benney-Luke equation, Physica D., 45 (1999), 476-496.       
16 J. G. Verwer, J. G. Blom and W. Hundsdorfer, An implicit-explicit approach for atmospheric transport-chemistry problems, Applied Numerical Mathematics, 20 (1996), 191-209.       
17 G. B. Whitham, Linear and Nonlinear Waves, Wiley-Interscience, 1974.       

Go to top