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A RUDN University mathematician has for the first time proved the theorem of existence and uniqueness of solutions of the Zakharov-Kuznetsov equation in a strip. Such theorems are very rare for partial differential equations. The new results can be applied in fields such as astrophysics, for instance, in describing the propagation of plane waves in plasma. The article is published in the journal Nonlinear Analysis: Real World Applications.
The Zakharov-Kuznetsov equation is a one-function equation of two variables x and y. For physics, x is the direction of wave propagation, and the deformation of the medium occurs along the perpendicular direction y. For example, in the oscillation of a guitar string, the wave appears to run down the string, while the oscillations occur perpendicularly relative to the run of the wave.
Number - Results - Solutions - Equations - Case
There are a large number of results that describe solutions of the Zakharov-Kuznetsov equations in the case when there are no constraints on y. But the question of wave propagation in the strip—when y is limited—was not extensively studied until recently.
RUDN University mathematicians dealt with the Zakharov-Kuznetsov equation in the strip. They examined three main cases—when there are no oscillations on the boundary of the strip, when there is no current on...
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