Browsing by Author "Yordanov, R. G."

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    Cauchy-problem for the linearized version of the Generalized Polynomial KdV equation
    Yordanov, R. G. (AIP Publishing, 1992-06)
    In the present paper results about the "Generalized Polynomial Korteweg-de Vries equation" (GPKdV) are obtained, extending the ones by Sachs [SIAM J. Math. Anal. 14, 674 (1983)] for the Korteweg-de Vries (KdV) equation. Namely, the evolution of the so-called "prolonged squared" eigenfunctions of the associated spectral problem according to the linearized GPKdV is proven, the Lax pairs associated with the "prolonged" eigenfunctions as well as "prolonged squared" eigenfunctions are derived, and on the basis of some expansion formulas the Cauchy problem for the linearized GPKdV with a decreasing at infinity initial condition is solved.
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    Why do soliton equations come in hierarchies?
    Yordanov, R. G. (AIP Publishing, 1993-09)
    In this article, an identity satisfied by the so-called recursion operator is derived. The identity generates by itself an infinite sequence of Lax pairs, thus ensuring the complete integrability of the corresponding hierarchy of nonlinear evolution equations. It is also shown that this identity yields the familiar property that the squares of eigenfunctions of the associated linear spectral problem satisfy the linearized version of the respective soliton equation.