EXPLICIT FORMULAS TO SOLUTIONS OF THE NONLINEAR SCHRODINGER EQUATION WITH POWER AND LOGARITHMIC TYPE NONLINEARITIES

被引：0

作者：

Popivanov, Petar ^{[1
]}

Slavova, Angela ^{[1
]}

机构：

[1] Bulgarian Acad Sci, Inst Math & Informat, Acad G Bonchev St,Bl 8, BU-1113 Sofia, Bulgaria

来源：

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES | 2019年 / 72卷 / 03期

关键词：

nonlinear Schrodinger equation; soliton and kink type solutions; hyperbolic and elliptic functions;

D O I：

10.7546/CRABS.2019.03.01

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

This paper deals with explicit formulas to the solutions of the generalized nonlinear derivative Schrodinger equation with power (polynomial) and logarithmic type nonlinearities. Then soliton and kink type solutions are constructed. To do this the inverse function of some function written into integral form must be found. In some cases it can be expressed by elementary or special functions (elliptic, hyperbolic). Possible applications are into laser optics.

引用

页码：283 / 291

页数：9

共 7 条

[1]

Arnold V., 1992, Ordinary Differential Equations

[2]

Dwight H. B., 1961, Tables of Integrals and Other Mathematical Data

[3] INSTABILITY OF SOLITARY WAVES FOR A GENERALIZED DERIVATIVE NONLINEAR SCHRODINGER EQUATION IN A BORDERLINE CASE [J].

Fukaya, Noriyoshi .

KODAI MATHEMATICAL JOURNAL, 2017, 40 (03) :450-467

[4] Mode-locked soliton lasers [J].

Kutz, J. Nathan .

SIAM REVIEW, 2006, 48 (04) :629-678

[5]

Pava JA, 2018, INDIANA U MATH J, V67, P471

[6]

POPIVANOV P, 2018, SERIES ANAL APPL COM, V9

[7]

2017, RIC MAT, V66, P531, DOI DOI 10.1007/S11587-017-0319-Y

← 1 →