Lax Pairs and Darboux Transformations for Euler Equations
نویسندگان
چکیده
منابع مشابه
Chaos in PDEs and Lax Pairs of Euler Equations
Recently, the author and collaborators have developed a systematic program for proving the existence of homoclinic orbits in partial differential equations. Two typical forms of homoclinic orbits thus obtained are: (1) transversal homoclinic orbits, (2) Silnikov homoclinic orbits. Around the transversal homoclinic orbits in infinite-dimensional autonomous systems, the author was able to prove t...
متن کاملDarboux Transformations for a Lax Integrable System in 2n-Dimensions
A 2n-dimensional Lax integrable system is proposed by a set of specific spectral problems. It contains Takasaki equations, the self-dual Yang-Mills equations and its integrable hierarchy as examples. An explicit formulation of Darboux transformations is established for this Lax integrable system. The Vandermonde and generalized Cauchy determinant formulas lead to a description for deriving expl...
متن کاملHigher-order Darboux transformations with foreign auxiliary equations and equivalence with generalized Darboux transformations
We show that a recently developed modified Darboux transformation that uses foreign auxiliary equations, can be unified with the Darboux transformation for generalized Schrödinger equations. As a consequence of this unification, we obtain explicit Darboux transformations with foreign auxiliary equations of arbitrary order. © 2012 Elsevier Ltd. All rights reserved.
متن کاملErgodic Isospectral Theory of the Lax Pairs of Euler Equations with Harmonic Analysis Flavor
Isospectral theory of the Lax pairs of both 3D and 2D Euler equations of inviscid fluids is developed. Eigenfunctions are represented through an ergodic integral. The Koopman group and mean ergodic theorem are utilized. Further harmonic analysis results on the ergodic integral are introduced. The ergodic integral is a limit of the oscillatory integral of the first kind.
متن کاملDarboux Transformations for Schrodinger Equations in Two Variables
Darboux transformations in one variable form the basis for the factorization methods and have numerous applications to geometry, nonlinear equations and SUSY quantum mechanics. In spite of this wide range of applications the theory of Darboux transformations in two variables and its elegant relationship to analytic complex functions has not been recognized in the literature. To close this gap w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Studies in Applied Mathematics
سال: 2003
ISSN: 0022-2526,1467-9590
DOI: 10.1111/1467-9590.t01-1-00229