We study a generalized higher-order nonlinear Schr¨odinger equation in an optical fiber or a planar waveguide.We obtain the Lax pair and N-fold Darboux transformation(DT)with N being a positive integer.Based on L...We study a generalized higher-order nonlinear Schr¨odinger equation in an optical fiber or a planar waveguide.We obtain the Lax pair and N-fold Darboux transformation(DT)with N being a positive integer.Based on Lax pair obtained by us,we derive the infinitely-many conservation laws.We give the bright one-,two-,and N-soliton solutions,and the first-,second-,and Nth-order breather solutions based on the N-fold DT.We conclude that the velocities of the bright solitons are influenced by the distributed gain function,g(z),and variable coefficients in equation,h1(z),p1(z),r1(z),and s1(z)via the asymptotic analysis,where z represents the propagation variable or spatial coordinate.We also graphically observe that:the velocities of the first-and second-order breathers will be affected by h1(z),p1(z),r1(z),and s1(z),and the background wave depends on g(z).展开更多
Damage caused by people and organizations unconnected with the pipeline management is a major risk faced by pipelines,and its consequences can have a huge impact.However,the present measures to monitor this have major...Damage caused by people and organizations unconnected with the pipeline management is a major risk faced by pipelines,and its consequences can have a huge impact.However,the present measures to monitor this have major problems such as time delays,overlooking threats,and false alarms.To overcome the disadvantages of these methods,analysis of big location data from mobile phone systems was applied to prevent third-party damage to pipelines,and a third-party damage prevention system was developed for pipelines including encryption mobile phone data,data preprocessing,and extraction of characteristic patterns.By applying this to natural gas pipelines,a large amount of location data was collected for data feature recognition and model analysis.Third-party illegal construction and occupation activities were discovered in a timely manner.This is important for preventing third-party damage to pipelines.展开更多
基金Project supported by the the Fundamental Research Funds for the Central Universities(Grant No.2023MS163).
文摘We study a generalized higher-order nonlinear Schr¨odinger equation in an optical fiber or a planar waveguide.We obtain the Lax pair and N-fold Darboux transformation(DT)with N being a positive integer.Based on Lax pair obtained by us,we derive the infinitely-many conservation laws.We give the bright one-,two-,and N-soliton solutions,and the first-,second-,and Nth-order breather solutions based on the N-fold DT.We conclude that the velocities of the bright solitons are influenced by the distributed gain function,g(z),and variable coefficients in equation,h1(z),p1(z),r1(z),and s1(z)via the asymptotic analysis,where z represents the propagation variable or spatial coordinate.We also graphically observe that:the velocities of the first-and second-order breathers will be affected by h1(z),p1(z),r1(z),and s1(z),and the background wave depends on g(z).
基金supported by Pipeline Management Data Analysis and Typical Model Research [Grant Number 2016B-3105-0501]CNPC (China National Petroleum Corporation) project, Research on Oil and Gas Pipeline Safety and Reliability Operating [Grant Number 2015-B025-0628]
文摘Damage caused by people and organizations unconnected with the pipeline management is a major risk faced by pipelines,and its consequences can have a huge impact.However,the present measures to monitor this have major problems such as time delays,overlooking threats,and false alarms.To overcome the disadvantages of these methods,analysis of big location data from mobile phone systems was applied to prevent third-party damage to pipelines,and a third-party damage prevention system was developed for pipelines including encryption mobile phone data,data preprocessing,and extraction of characteristic patterns.By applying this to natural gas pipelines,a large amount of location data was collected for data feature recognition and model analysis.Third-party illegal construction and occupation activities were discovered in a timely manner.This is important for preventing third-party damage to pipelines.
