Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 75, 2000 - Issue 1-2
Submit an article Journal homepage
95
Views
34
CrossRef citations to date
0
Altmetric
Original Articles

Solitary-wave and multi-pulsed traveling-wave solutions of boussinesq systems

Min Chen Department of Mathematics , Penn State University, University Park, Pa, 16802, USA
Pages 213-240 | Received 01 Aug 1999, Published online: 25 Nov 2010

Citations (34)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (1)

Juan Carlos Muñoz Grajales. (2012) Decay of solutions of a Boussinesq-type system with variable coefficients. Waves in Random and Complex Media 22:4, pages 589-612.
Read now

Articles from other publishers (33)

Kanyuta Poochinapan & Ben Wongsaijai. (2023) High-performance computing of structure-preserving algorithm for the coupled BBM system formulated by weighted compact difference operators. Mathematics and Computers in Simulation 205, pages 439-467.
Crossref
Robin Ming Chen & Jie Jin. (2022) Global bifurcation of solitary waves to the Boussinesq abcd system. Journal of Differential Equations 310, pages 235-263.
Crossref
Hung Luong & Jean-Claude Saut. (2022) The Boussinesq systems on the background of a line solitary wave. Discrete and Continuous Dynamical Systems 0:0, pages 0-0.
Crossref
Vassilios A. Dougalis, Angel Durán & Leetha Saridaki. (2021) On solitary-wave solutions of Boussinesq/Boussinesq systems for internal waves. Physica D: Nonlinear Phenomena 428, pages 133051.
Crossref
M. Ali Akbar, Lanre Akinyemi, Shao-Wen Yao, Adil Jhangeer, Hadi Rezazadeh, Mostafa M.A. Khater, Hijaz Ahmad & Mustafa Inc. (2021) Soliton solutions to the Boussinesq equation through sine-Gordon method and Kudryashov method. Results in Physics 25, pages 104228.
Crossref
Dimitrios Mitsotakis, Hendrik Ranocha, David I. Ketcheson & Endre Süli. (2021) A Conservative Fully Discrete Numerical Method for the Regularized Shallow Water Wave Equations. SIAM Journal on Scientific Computing 43:2, pages B508-B537.
Crossref
Theodoros Katsaounis, Dimitrios Mitsotakis & Georges Sadaka. (2020) Boussinesq-Peregrine water wave models and their numerical approximation. Journal of Computational Physics 417, pages 109579.
Crossref
Neng Zhu, Zhengrong Liu & Kun Zhao. (2019) Non blowup of a generalized Boussinesq–Burgers system with nonlinear dispersion relation and large data. Physica D: Nonlinear Phenomena 392, pages 81-98.
Crossref
Dimitrios Mitsotakis, Denys Dutykh & Qian Li. (2018) Asymptotic nonlinear and dispersive pulsatile flow in elastic vessels with cylindrical symmetry. Computers & Mathematics with Applications 75:11, pages 4022-4047.
Crossref
Neng Zhu, Zhengrong Liu & Kun Zhao. (2018) On the Boussinesq–Burgers equations driven by dynamic boundary conditions. Journal of Differential Equations 264:3, pages 2287-2309.
Crossref
Ellen ShiTing Bao, Robin Ming Chen & Qing Liu. (2014) Existence and Symmetry of Ground States to the Boussinesq abcd Systems. Archive for Rational Mechanics and Analysis 216:2, pages 569-591.
Crossref
Dimitrios Mitsotakis, Boaz Ilan & Denys Dutykh. (2014) On the Galerkin/Finite-Element Method for the Serre Equations. Journal of Scientific Computing 61:1, pages 166-195.
Crossref
D. Tseluiko, M. Galvagno & U. Thiele. (2014) Collapsed heteroclinic snaking near a heteroclinic chain in dragged meniscus problems. The European Physical Journal E 37:4.
Crossref
Denys Dutykh & Didier Clamond. (2014) Efficient computation of steady solitary gravity waves. Wave Motion 51:1, pages 86-99.
Crossref
Angel Duran, Denys Dutykh & Dimitrios Mitsotakis. (2013) On the Galilean Invariance of Some Nonlinear Dispersive Wave Equations. Studies in Applied Mathematics 131:4, pages 359-388.
Crossref
Robin Ming Chen & Yue Liu. (2013) On the ill-posedness of a weakly dispersive one-dimensional Boussinesq system. Journal d'Analyse Mathématique 121:1, pages 299-316.
Crossref
Sevdzhan Hakkaev, Milena Stanislavova & Atanas Stefanov. (2013) Spectral Stability for Subsonic Traveling Pulses of the Boussinesq “abc" System. SIAM Journal on Applied Dynamical Systems 12:2, pages 878-898.
Crossref
Jianke Yang. (2012) Classification of Solitary Wave Bifurcations in Generalized Nonlinear Schrödinger Equations. Studies in Applied Mathematics 129:2, pages 133-162.
Crossref
Jianke Yang. (2012) No stability switching at saddle-node bifurcations of solitary waves in generalized nonlinear Schrödinger equations. Physical Review E 85:3.
Crossref
D.C. Antonopoulos & V.A. Dougalis. (2012) Numerical solution of the ‘classical’ Boussinesq system. Mathematics and Computers in Simulation 82:6, pages 984-1007.
Crossref
Jianke Yang. 2013. Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations. Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations 639 655 .
Denys Dutykh, Theodoros Katsaounis & Dimitrios Mitsotakis. (2011) Finite volume schemes for dispersive wave propagation and runup. Journal of Computational Physics 230:8, pages 3035-3061.
Crossref
D.C. Antonopoulos, V.A. Dougalis & D.E. Mitsotakis. (2010) Numerical solution of Boussinesq systems of the Bona–Smith family. Applied Numerical Mathematics 60:4, pages 314-336.
Crossref
Min Chen, Christopher W. Curtis, Bernard Deconinck, Crystal W. Lee & Nghiem Nguyen. (2010) Spectral Stability of Stationary Solutions of a Boussinesq System Describing Long Waves in Dispersive Media. SIAM Journal on Applied Dynamical Systems 9:3, pages 999-1018.
Crossref
Yacheng Liu & Runzhang Xu. (2008) Global existence and blow up of solutions for Cauchy problem of generalized Boussinesq equation. Physica D: Nonlinear Phenomena 237:6, pages 721-731.
Crossref
J. Knobloch & T. Wagenknecht. (2008) Snaking of Multiple Homoclinic Orbits in Reversible Systems. SIAM Journal on Applied Dynamical Systems 7:4, pages 1397-1420.
Crossref
V. A. Dougalis, A. Durán, M. A. López-Marcos & D. E. Mitsotakis. (2007) A Numerical Study of the Stability of Solitary Waves of the Bona–Smith Family of Boussinesq Systems. Journal of Nonlinear Science 17:6, pages 569-607.
Crossref
Vassilios A. Dougalis, Dimitrios E. Mitsotakis & Jean-Claude Saut. (2007) On some Boussinesq systems in two space dimensions: theory and numerical analysis. ESAIM: Mathematical Modelling and Numerical Analysis 41:5, pages 825-854.
Crossref
Chen Chun-Li, Zhang Jin E & Li Yi-Shen. (2007) Study on an extended Boussinesq equation. Chinese Physics 16:8, pages 2167-2179.
Crossref
David A W Barton, Bernd Krauskopf & R Eddie Wilson. (2007) Homoclinic bifurcations in a neutral delay model of a transmission line oscillator. Nonlinearity 20:4, pages 809-829.
Crossref
J. Knobloch & T. Wagenknecht. (2005) Homoclinic snaking near a heteroclinic cycle in reversible systems. Physica D: Nonlinear Phenomena 206:1-2, pages 82-93.
Crossref
J L Bona, M Chen & J-C Saut. (2004) Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory. Nonlinearity 17:3, pages 925-952.
Crossref
M. Chen. (2003) Equations for bi-directional waves over an uneven bottom. Mathematics and Computers in Simulation 62:1-2, pages 3-9.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.