Asymptotic soliton-like solutions of the nonlinear Schr�dinger equation with variable coefficients

1983 ◽  
Vol 56 (1) ◽  
pp. 661-668
Author(s):  
V. Yu. Subochev ◽  
V. A. Tsupin
Keyword(s):  
Variable Coefficients ◽  
Dinger Equation ◽  
Asymptotic Soliton

Asymptotic soliton-like solutions to the Benjamin–Bona–Mahony equation with variable coefficients and a strong singularity

2021 ◽  
Vol 18 (2) ◽  
pp. 226-242
Author(s):  
Valerii Samoilenko ◽  
Yuliia Samoilenko
Keyword(s):  
Asymptotic Solution ◽  
Small Parameter ◽  
Order Term ◽  
Variable Coefficients ◽  
Main Term ◽  
Qualitative Properties ◽  
First Order ◽  
Strong Singularity ◽  
Non Linear ◽  
Asymptotic Soliton

The paper deals with constructing an asymptotic one-phase soliton-like solution to the Benjamin--Bona--Mahony equation with variable coefficients and a strong singularity making use of the non-linear WKB technique. The influence of the small-parameter value on the structure and the qualitative properties of the asymptotic solution, as well as the accuracy with which the solution satisfies the considerable equation, have been analyzed. It was demonstrated that due to the strong singularity, it is possible to write explicitly not only the main term of the asymptotics but at least its first-order term.

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