Trilinear equations, Bell polynomials, and resonant solutions
نویسنده
چکیده
A class of trilinear differential operators is introduced through a technique of assigning signs to derivatives and used to create trilinear differential equations. The resulting trilinear differential operators and equations are characterized by the Bell polynomials, and the superposition principle is applied to the construction of resonant solutions of exponential waves. Two illustrative examples are made by an algorithm using weights of dependent variables.
منابع مشابه
Numerical solution of nonlinear Fredholm-Volterra integral equations via Bell polynomials
In this paper, we propose and analyze an efficient matrix method based on Bell polynomials for numerically solving nonlinear Fredholm- Volterra integral equations. For this aim, first we calculate operational matrix of integration and product based on Bell polynomials. By using these matrices, nonlinear Fredholm-Volterra integral equations reduce to the system of nonlinear algebraic equations w...
متن کاملBilinear equations, Bell polynomials and linear superposition principle
A class of bilinear differential operators is introduced through assigning appropriate signs and used to create bilinear differential equations which generalize Hirota bilinear equations. The resulting bilinear differential equations are characterized by a special kind of Bell polynomials and the linear superposition principle is applied to the construction of their linear subspaces of solution...
متن کاملViewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials
In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.
متن کامل0 A Generalization of the Submodel of Nonlinear C P 1 Models
We generalize the submodel of nonlinear CP 1 models. The generalized models include higher order derivatives. For the systems of higher order equations, we construct a Bäcklund-like transformation of solutions and an infinite number of conserved currents by using the Bell polynomials.
متن کاملBernoulli collocation method with residual correction for solving integral-algebraic equations
The principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. This method gives an analytic solution when ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013