RAPIDLY DECREASING SOLUTION OF THE INITIAL BOUNDARY-VALUE PROBLEM FOR AN INFINITE SYSTEM OF NONLINEAR EVOLUTION EQUATIONS

Məmmədova A.

Advanced Mathematical Models and Applications, vol.10, no.1, pp.81-87, 2025 (Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 10 Say: 1
  • Nəşr tarixi: 2025
  • Doi nömrəsi: 10.62476/amma.10181
  • jurnalın adı: Advanced Mathematical Models and Applications
  • Jurnalın baxıldığı indekslər: Scopus
  • Səhifə sayı: pp.81-87
  • Açar sözlər: Langmuir model, method of inverse spectral problem, nonlinear evolution equation, rapidly decreasing soluition, scattering data
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

An initial boundary-value problem with zero boundary condition for an infnite system of nonlinear evolution equations is considered. First, the scattering problem for a second-order difference equation, which is related to the problem under consideration, was considered. We prove the existence and uniqueness of a rapidly decreasing solution and determine a class of initial data that guarantees the existence of a rapidly decreasing solution. Then, the scattering problem is considered for a second-order difference equation whose coefficients are solutions to a nonlinear equation. A law of variation of scattering data with time has been found. Using the variation of the scattering data and by the inverse spectral method, an algorithm for constructing the solution is obtained.