The Modified Korteweg-de Vries Hierarchy: Lax Pair Representation and Bi-Hamiltonian Structure
نویسندگان
چکیده
منابع مشابه
Korteweg-de Vries hierarchy and related
We consider complementary dynamical systems related to stationary Korteweg-de Vries hierarchy of equations. A general approach for finding elliptic solutions is given. The solutions are expressed in terms of Novikov polynomials in general quasi-periodic case. For periodic case these polynomials coincide with Hermite and Lamé polynomials. As byproduct we derive 2 × 2 matrix Lax representation fo...
متن کاملNumerical inverse scattering for the Korteweg–de Vries and modified Korteweg–de Vries equations
Recent advances in the numerical solution of Riemann–Hilbert problems allow for the implementation of a Cauchy initial value problem solver for the Korteweg–de Vries equation (KdV) and the defocusing modified Korteweg–de Vries equation (mKdV), without any boundary approximation. Borrowing ideas from the method of nonlinear steepest descent, this method is demonstrated to be asymptotically accur...
متن کاملOn the heat kernel and the Korteweg--de Vries hierarchy
L’accès aux articles de la revue « Annales de l’institut Fourier » (http://aif.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://aif.cedram.org/legal/). Toute reproduction en tout ou partie cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation à fin strictement personnelle du copiste est constitutive d’une infraction pénale. Toute c...
متن کاملSupersymmetric quantum mechanics and the Korteweg-de Vries hierarchy
The connection between supersymmetric quantummechanics and the Kortewegde Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction o...
متن کاملThe Korteweg-de Vries Hierarchy and Long Water-Waves
By using the multiple scale method with the simultaneous introduction of multiple times, we study the propagation of long surface-waves in a shallow inviscid fluid. As a consequence of the requirements of scale invariance and absence of secular terms in each order of the perturbative expansion, we show that the Korteweg-de Vries hierarchy equations do appear in the description of such waves. Fi...
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: Zeitschrift für Naturforschung A
سال: 2009
ISSN: 1865-7109,0932-0784
DOI: 10.1515/zna-2009-3-403