Classification of the travelling waves in the nonlinear dispersive KdV equation (Q975846)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Classification of the travelling waves in the nonlinear dispersive KdV equation |
scientific article; zbMATH DE number 5720176
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Classification of the travelling waves in the nonlinear dispersive KdV equation |
scientific article; zbMATH DE number 5720176 |
Statements
Classification of the travelling waves in the nonlinear dispersive KdV equation (English)
0 references
11 June 2010
0 references
The traveling wave solutions of the Korteweg-de Vries-like equation (\(K(2,2)\)) \[ u_t + a(u^2)_x + (u^2)_{xxx} =0 \] modeling the formation of pattern in nonlinear dispersion, are investigated. Besides the known compacton solutions (compactly supported solitons with nonsmooth fronts), the equation is shown to admit other different types of solutions too, such as cuspons, peakons, loopons, stumpons and fractal-like waves. A qualitative analysis of the traveling waves, as well as their classification, is carried on. Finally, some new explicit solutions are given.
0 references
traveling wave solutions
0 references
nonlinear dispersive equations
0 references
pattern formation
0 references
solitons
0 references
0 references
0 references
0 references
0 references
0 references
0 references
0 references
