Seminar talk, 1 March 2017: Difference between revisions
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| title = Reflections of soliton on viscous barrier and the degradation of conserved quantities for the KdV | | title = Reflections of soliton on viscous barrier and the degradation of conserved quantities for the KdV | ||
| abstract = If waves are described by the equation | | abstract = If waves are described by the equation | ||
u_t=2uu_x+ | |||
where \chi_{a,b} characteristic function of the interval [a,b], then the soliton 6a^2 ch^{-2} (4a^3t+ax) arrived from the right partially reflects at viscous barrier and partially | <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\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.