Presentation of special series with computed recurrently coefficients of solutions of nonlinear evolution equations

All-Russian conference on Nonlinear Waves: Theory and New Applications

Filimonov, M.^1,2 ; Masih, A.^3

Ural State University, Ekterinburg, Russia^1

Institute of Mathematics and Mechanics of UrB RAS, Ekaterinburg, Russia^2

Quaid-e-Azam University Islamabad, Pakistan^3

关键词: Analytical method;    Arbitrary functions;    Basis functions;    Global conver-gence;    Linear differential equation;    Nonlinear evolution equation;    Nonlinear partial differential equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/722/1/012040/pdf
DOI  :  10.1088/1742-6596/722/1/012040

来源: IOP

【 摘 要 】

One of the analytical methods of presenting solutions of nonlinear partial differential equations is the method of special series in powers of specially selected functions called basis functions. The coefficients of such series are found successively as solutions of linear differential equations. To find recurrence, the coefficient is achieved by the choice of basis functions, which may also contain arbitrary functions. By using such functional arbitrariness, it allows in some cases to prove the global convergence of the corresponding constructed series, as well as the solvability of the boundary value problem.