Ellipticity Conditions for the Lax Operator of the Kp Equations
نویسندگان
چکیده
The Lax pseudo-differential operator plays a key role in studying the general set of KP equations, although it is normally treated in a formal way, without worrying about a complete characterization of its mathematical properties. The aim of the present paper is therefore to investigate the ellipticity condition. For this purpose, after a careful evaluation of the kernel with the associated symbol, the majorization ensuring ellipticity is studied in detail. This leads to non-trivial restrictions on the admissible set of potentials in the Lax operator. When their time evolution is also considered, the ellipticity conditions turn out to involve derivatives of the logarithm of the τ -function. PACS numbers: 05.45.Y
منابع مشابه
A Lax Operator Hierarchy for the New Fifth Order Integrable System
We consider the Lax representation of the new two-component coupled integrable system recently discovered by the author. Connection of the hierarchy of infinitely many Lax pairs with each other is presented.
متن کاملOn Dispersionless Hirota Type Equations
Various connections between 2-D gravity and KdV, dKdV, inverse scattering, etc. are established. For KP we show how to extract from the dispersionless limit of the Fay differential identity of Takasaki-Takebe the collection of differential equations for F = log(τ ) which play the role of Hirota type equations in the dispersionless theory. 1. HIROTA EQUATIONS In [7] we showed how second derivati...
متن کاملHermitian solutions to the system of operator equations T_iX=U_i.
In this article we consider the system of operator equations T_iX=U_i for i=1,2,...,n and give necessary and suffcient conditions for the existence of common Hermitian solutions to this system of operator equations for arbitrary operators without the closedness condition. Also we study the Moore-penrose inverse of a ncross 1 block operator matrix and. then gi...
متن کاملar X iv : s ol v - in t / 9 70 70 14 v 1 2 7 Ju l 1 99 7 The constrained modified KP hierarchy and the generalized Miura transformations
In this letter, we consider the second Hamiltonian structure of the constrained modified KP hierarchy. After mapping the Lax operator to a pure differential operator the second structure becomes the sum of the second and the third Gelfand-Dickey brackets defined by this differential operator. We simplify this Hamiltonian structure by factorizing the Lax operator into linear terms.
متن کاملExtended Conformal Algebras Associated with Constrained KP Hierarchy
We examine the conformal preperty of the second Hamiltonian structure of constrained KP hierarchy derived by Oevel and Strampp. We find that it naturally gives a family of nonlocal extended conformal algebras. We give two examples of such algebras and find that they are similar to Bilal's V algebra. By taking a gauge transformation one can map the constrained KP hierarchy to Kupershmidt's nonst...
متن کامل