Explicit Solutions for a Class of Nonlinear PDEs that Arise in Allocation Problems

2008 ◽  
Vol 39 (5) ◽  
pp. 1627-1667
Author(s):  
Paul Dupuis ◽  
Jim X. Zhang
Keyword(s):  
Nonlinear Pdes ◽  
Explicit Solutions ◽  
Allocation Problems

scholarly journals Explicit solutions of some equations and systems of mathematical physics

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Angela Slavova ◽  
Petar Popivanov
Keyword(s):  
Nonlinear Partial Differential Equations ◽  
Elliptic Functions ◽  
Mathematical Physics ◽  
Global Solvability ◽  
Nonlinear Pdes ◽  
Heisenberg Ferromagnet ◽  
Explicit Solutions ◽  
Evolution System ◽  
Integrable Evolution ◽  
Classical Heisenberg Ferromagnet Equation

Abstract This paper deals at first with a fully integrable evolution system of nonlinear partial differential equations (PDEs) which is a generalization of the classical Heisenberg ferromagnet equation. Then the scalar variant of this system is considered. Looking for solutions of special form, the problem of finding explicit solutions of the above-mentioned equations is reduced to the global solvability of overdetermined real-valued systems of nonlinear PDEs. In many cases particular solutions which are not solitons are expressed by classical functions including some special ones as Jacobi elliptic functions, Legendre elliptic functions, and Weierstrass normal elliptic integrals. A geometrical visualization of several solutions is also proposed.

Explicit Solutions for a General Class of Optimal Allocation Problems

2013 ◽  
Author(s):  
Ka Chun Cheung ◽  
Jan Dhaene ◽  
Yian Vivian Rong ◽  
S. C. P. Yam
Keyword(s):  
General Class ◽  
Optimal Allocation ◽  
Explicit Solutions ◽  
Allocation Problems

scholarly journals ON p – q DUALITY AND EXPLICIT SOLUTIONS IN c ≤ 1 2D GRAVITY MODELS

1995 ◽  
Vol 10 (08) ◽  
pp. 1219-1236 ◽  
Author(s):  
S. KHARCHEV ◽  
A. MARSHAKOV
Keyword(s):  
String Theory ◽  
Exact Solutions ◽  
2D Gravity ◽  
Integral Formula ◽  
Integral Representations ◽  
Gravity Models ◽  
Explicit Solutions ◽  
String Equation ◽  
Duality Transformation

We study the role of integral representations in the description of nonperturbative solutions to c ≤ 1 string theory. A generic solution is determined by two functions, W(x) and Q(x), which behave at infinity like xp and xq respectively. The integral formula for arbitrary (p, q) models is derived, which explicitly realizes a duality transformation between (p, q) and (q, p) 2D gravity solutions. We also discuss the exact solutions to the string equation and reduction condition and present several explicit examples.

Complexity of Allocation Problems in Spectrum Markets with Interference Complementarities

2013 ◽  
Vol 31 (3) ◽  
pp. 489-499 ◽  
Author(s):  
Hang Zhou ◽  
Randall Berry ◽  
Michael L. Honig ◽  
Rakesh Vohra
Keyword(s):  
Allocation Problems ◽  
Spectrum Markets

Explicit Solutions of the Coupled Bogoyavlensky Lattice 1(2) Hierarchy

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Xianguo Geng ◽  
Wei Liu ◽  
Bo Xue
Keyword(s):  
Explicit Solutions
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