Exact traveling waves solutions for long waves and blow-up phenomena
DOI10.7153/dea-08-32zbMath1351.35127OpenAlexW2514777509MaRDI QIDQ2823239
Pedro Gamboa, Xavier Carvajal, Octavio P. Vera Villagrán
Publication date: 6 October 2016
Published in: Differential Equations & Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.7153/dea-08-32
BBM equationKdV equationCauchy problemslocal \& global well-posednessnonlinear dispersive wave equationswater wave modelsbenney-lin equation
PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44) Traveling wave solutions (35C07)
Cites Work
- Comparison between model equations for long waves and blow-up phenomena
- Well-posedness and blow-up phenomena for a higher order shallow water equation
- Well-posedness for regularized nonlinear dispersive wave equations
- Well-posedness for the fifth-order shallow water equations
- Comparisons between model equations for long waves
- Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory
- Comparisons between the BBM equation and a Boussinesq system
- Existence of blow-up solutions in the energy space for the critical generalized KdV equation
- Approximate Equations for Long Nonlinear Waves on a Viscous Fluid
- A General Theory for Interactions Between Short and Long Waves
- Blow up in finite time and dynamics of blow up solutions for the 𝐿²–critical generalized KdV equation
- Comparison of model equations for small-amplitude long waves
- Finite amplitude side-band stability of a viscous film
- Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory
- Well-posedness and ill-posedness of the fifth order modifed KdV equation
- Well-posedness for the fifth-order KdV equation in the energy space
- Model equations for long waves in nonlinear dispersive systems
- Hamiltonian long‐wave expansions for free surfaces and interfaces
This page was built for publication: Exact traveling waves solutions for long waves and blow-up phenomena
