scholarly journals Singular fiber of the Mumford system and rational solutions to the KdV hierarchy

2009 ◽  
pp. NA-NA
Author(s):  
Rei Inoue ◽  
Takao Yamazaki ◽  
Pol Vanhaecke
Keyword(s):  
Rational Solutions ◽  
Kdv Hierarchy ◽  
Singular Fiber

scholarly journals On tau-functions for the KdV hierarchy

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Boris Dubrovin ◽  
Di Yang ◽  
Don Zagier
Keyword(s):  
Tau Functions ◽  
Kdv Hierarchy

scholarly journals ON PROPERTIES OF FINITE-ORDER MEROMORPHIC SOLUTIONS OF A CERTAIN DIFFERENCE PAINLEVÉ I EQUATION

2011 ◽  
Vol 85 (3) ◽  
pp. 463-475 ◽  
Author(s):  
MEI-RU CHEN ◽  
ZONG-XUAN CHEN
Keyword(s):  
Finite Order ◽  
Meromorphic Solutions ◽  
Rational Solutions ◽  
Polynomial Solutions ◽  
The Difference ◽  
Image Position

AbstractIn this paper, we investigate properties of finite-order transcendental meromorphic solutions, rational solutions and polynomial solutions of the difference Painlevé I equation where a, b and c are constants, ∣a∣+∣b∣≠0.

scholarly journals REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KdV HIERARCHIES AND THE TWO-MATRIX MODEL

1995 ◽  
Vol 10 (17) ◽  
pp. 2537-2577 ◽  
Author(s):  
H. ARATYN ◽  
E. NISSIMOV ◽  
S. PACHEVA ◽  
A.H. ZIMERMAN
Keyword(s):  
Poisson Bracket ◽  
Hamiltonian Structure ◽  
Toda Lattice ◽  
Free Field ◽  
String Model ◽  
Matrix Formulation ◽  
Hamiltonian Action ◽  
Kdv Hierarchy ◽  
Associated Matrix ◽  
Toda Lattice Hierarchy

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL (M+1, M−k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL (M+1, M−k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M−k) Poisson bracket algebras generalizing the familiar nonlinear WM+1 algebra. Discrete Bäcklund transformations for SL (M+1, M−k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL (M+1, 1) KdV hierarchy.

Rational solutions of the KdV equation with damping

1979 ◽  
Vol 24 (4) ◽  
pp. 97-100 ◽  
Author(s):  
F. Calogero ◽  
M. A. Olshanetsky ◽  
A. M. Perelomov
Keyword(s):  
Kdv Equation ◽  
Rational Solutions ◽  
The Kdv Equation

RATIONAL SOLUTIONS OF THE BOUSSINESQ EQUATION

2008 ◽  
Vol 06 (04) ◽  
pp. 349-369 ◽  
Author(s):  
PETER A. CLARKSON
Keyword(s):  
Infinite Number ◽  
Boussinesq Equation ◽  
Nonlinear Schrödinger Equations ◽  
Schrödinger Equations ◽  
Rational Solutions ◽  
Painleve Equations ◽  
Special Polynomials ◽  
Symmetry Reductions ◽  
Nonlinear Schrodinger Equations ◽  
De Vries

Rational solutions of the Boussinesq equation are expressed in terms of special polynomials associated with rational solutions of the second and fourth Painlevé equations, which arise as symmetry reductions of the Boussinesq equation. Further generalized rational solutions of the Boussinesq equation, which involve an infinite number of arbitrary constants, are derived. The generalized rational solutions are analogs of such solutions for the Korteweg–de Vries and nonlinear Schrödinger equations.

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