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In most of the studies concerning nonlinear wave equations of Korteweg-de Vries type, the authors focus on waves of elevation. Such waves have general form uu(x, t) = Af(x−vt), where… Click to show full abstract
In most of the studies concerning nonlinear wave equations of Korteweg-de Vries type, the authors focus on waves of elevation. Such waves have general form uu(x, t) = Af(x−vt), where A > 0. In this communication we show that if uup(x, t) = Af(x− vt) is the solution of a given nonlinear equation, then udown(x, t) = −Af(x− vt), that is, an inverted wave is the solution of the same equation, but with changed sign of the parameter α. This property is common for KdV, extended KdV, fifth-order KdV, Gardner equations, and generalizations for cases with an uneven bottom.
Journal Title: Acta Physica Polonica A
Year Published: 2021
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