Seminar talk, 1 March 2017: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| (2 intermediate revisions by the same user not shown) | |||
| Line 6: | Line 6: | ||
<math>u_t=2uu_x+u_{xxx}+\varepsilon\chi_{a,b}u_{xx}</math>, | <math>u_t=2uu_x+u_{xxx}+\varepsilon\chi_{a,b}u_{xx}</math>, | ||
where <math>\chi_{a,b}</math> is the characteristic function of the interval <math>[a,b]</math>, then the soliton <math>6a^2\ | where <math>\chi_{a,b}</math> is the characteristic function of the interval <math>[a,b]</math>, then the soliton <math>6a^2\mathrm{ch}^{-2}(4a^3t+ax)</math> arrived from the right partially reflects at viscous barrier <math>x\in[a,b]</math> and partially passes through in the form of a soliton of smaller velocity and amplitude. The process in some degree is described by the so-called balance laws, which are the evolution of conservation laws for KdV. | ||
| video = | | video = | ||
| slides = | | slides = | ||
Latest revision as of 23:28, 22 February 2017
Speaker: Alexey Samokhin
Title: Reflections of soliton on viscous barrier and the degradation of conserved quantities for the KdV
Abstract:
If waves are described by the equation
,
where is the characteristic function of the interval , then the soliton arrived from the right partially reflects at viscous barrier and partially passes through in the form of a soliton of smaller velocity and amplitude. The process in some degree is described by the so-called balance laws, which are the evolution of conservation laws for KdV.
![{\displaystyle [a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c4b788fc5c637e26ee98b45f89a5c08c85f7935)
![{\displaystyle x\in [a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/026357b404ee584c475579fb2302a4e9881b8cce)