Results 241 to 250 of about 6,108,581 (281)

Pfaffianization of the Differential-Difference KP Equation

Journal of the Physical Society of Japan, 2004
Summary: We present an integrable coupled differential-difference Kadomtsev-Peviashvili equation, which is derived by extending Ohta and Hirota's Pfaffianization procedure to the differential-difference KP equation. Some Lie symmetries of this resulting system are also presented explicitly.
Xing-Biao Hu, Chun-Xia Li, Jun-Xiao Zhao
exaly   +3 more sources

A Differential-Difference Equation

SIAM Journal on Mathematical Analysis, 1987
Wimp showed that the hypergeometric polynomials \[ P_n (z) = {}_{p + 2} F_{p + 1} ( - n,n + \lambda ,a_{\bf p} ;b_{{\bf p} + 1} ;z),\quad n = 0,1, \cdots , \] satisfied a certain differential-difference equation. Here we show that all “common” solutions to the standard differential equation and the standard difference equation satisfied by the $P_n (z)$
Fields, Jerry L., Al-Salam, Waleed A.
openaire   +2 more sources

Nonlinear differential−difference equations

Journal of Mathematical Physics, 1975
A method is presented which enables one to obtain and solve certain classes of nonlinear differential−difference equations. The introduction of a new discrete eigenvalue problem allows the exact solution of the self−dual network equations to be found by inverse scattering.
Ablowitz, M. J., Ladik, F.
openaire   +1 more source

Differential-Difference Equations with Optimal Parameters

Computational Mathematics and Mathematical Physics, 2023
The paper considers difference schemes with optimal parameters for solving Maxwell’s equations. Using Laguerre transforms, the numerical values of the optimal parameters are determined and differential-difference equations are constructed. Differential-difference equations are solved by the finite-difference method with iterations over small optimal ...
openaire   +2 more sources

RELAXATION CYCLES OF DIFFERENTIAL-DIFFERENCE EQUATIONS

Russian Academy of Sciences. Izvestiya Mathematics, 1993
Summary: Equations of this type are widely used in the mathematical modeling of many biophysical processes. An informative example from mathematical ecology is used below to expound ways for constructing the asymptotics of their relaxation cycles of finite amplitude, along with methods of asymptotic integration of variational equations.
Kolesov, A. Yu., Kolesov, Yu. S.
openaire   +1 more source

BIFURCATION ANALYSIS OF DIFFERENTIAL-DIFFERENCE-ALGEBRAIC EQUATIONS

International Journal of Bifurcation and Chaos, 2004
The dynamics of differential-difference-algebraic equations is studied. The paper extends the study of the local bifurcations to transcritical and pitchfork bifurcation under certain nondegenerate conditions using Lyapunov–Schmidt reduction. Furthermore, an improved version of singularity induced bifurcation theorem is given in this paper.
Dongyun Du, Yun Tang
openaire   +2 more sources

Explicit solutions for a hierarchy of differential–difference equations

Applied Mathematics and Computation, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dong Gong, Xianguo Geng
openaire   +1 more source

New solutions to the differential-difference KP equation

Applied Mathematics Letters, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xue-Ru Wang, Junyi Zhu 0004, Zhijun Qiao
openaire   +1 more source

On existence of solutions of differential‐difference equations

Mathematical Methods in the Applied Sciences, 2015
This paper applies Nevanlinna theory of value distribution to discuss existence of solutions of certain types of non‐linear differential‐difference equations such as (5) and (8) given in the succeeding paragraphs. Existence of solutions of differential equations and difference equations can be said to have been well studied, that of differential ...
openaire   +2 more sources

Linear differential difference equations

2021
The paper introduces the subject through linear differential difference equations of retarded and neutral type with constant coefficients. There is a series of theories of linear equations with constant coefficients, the simplest possible differential difference equations, are based on such fundamental methods.
openaire   +1 more source