Seminar talk, 1 March 2017: Difference between revisions

Latest revision as of 23:28, 22 February 2017

Title: Reflections of soliton on viscous barrier and the degradation of conserved quantities for the KdV

Abstract:
If waves are described by the equation

$u_{t}=2uu_{x}+u_{xxx}+\varepsilon \chi _{a,b}u_{xx}$ ,

where $\chi _{a,b}$ is the characteristic function of the interval $[a,b]$ , then the soliton $6a^{2}\mathrm {ch} ^{-2}(4a^{3}t+ax)$ arrived from the right partially reflects at viscous barrier $x\in [a,b]$ 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.

@@ Line 3: / Line 3: @@
 | title = Reflections of soliton on viscous barrier and the degradation of conserved quantities for the KdV
 | abstract = If waves are described by the equation
-u_t=2uu_x+u_xxx+ \epsilon \chi_{a,b} u_xx,
-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 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.
+<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 =
 | slides =

Seminar talk, 1 March 2017: Difference between revisions

Latest revision as of 23:28, 22 February 2017

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