Seminar talk, 1 March 2017: Difference between revisions

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| abstract = If waves are described by the equation
| abstract = If waves are described by the equation


<math>u_t=2uu_x+u_{xxx}+\epsilon\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> characteristic function of the interval <math>[a,b]</math>, then the soliton <math>6a^2\mathop{ch}^{-2}(4a^3t+ax)</math> arrived from the right partially reflects at viscous barrier <math>x\in[a,b]</math> and partially pass through in the form of 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.
where <math>\chi_{a,b}</math> characteristic function of the interval <math>[a,b]</math>, then the soliton <math>6a^2\mathop{ch}^{-2}(4a^3t+ax)</math> arrived from the right partially reflects at viscous barrier <math>x\in[a,b]</math> and partially pass through in the form of 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.

Revision as of 23:26, 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 characteristic function of the interval , then the soliton arrived from the right partially reflects at viscous barrier and partially pass through in the form of 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.

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