The explicit solutions to the nonlinear Dirac equation and Dirac-Klein-Gordon equation

被引：24

作者：

Machihara, Shuji ^{[1
]}

Omoso, Takayuki ^{[1
]}

机构：

[1] Shimane Univ, Dept Math, Matsue, Shimane 6908504, Japan

来源：

RICERCHE DI MATEMATICA | 2007年 / 56卷 / 01期

关键词：

Nonlinear Dirac equation; Dirac-Klein-Gordon equation; Pauli matrix;

D O I：

10.1007/s11587-007-0002-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In [3] Dias and Figueira have reported that the square of the solution for the nonlinear Dirac equation satisfies the linear wave equation in one space dimension. So the aim of this paper is to proceed with their work and to clarify a structure of the nonlinear Dirac equation. The explicit solutions to the nonlinear Dirac equation and Dirac-Klein-Gordon equation are obtained.

引用

页码：19 / 30

页数：12

共 50 条

[21] On the concentration of semi-classical states for a nonlinear Dirac-Klein-Gordon system
Ding, Yanheng
Xu, Tian
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (03) : 1264 - 1294
[22] LOW REGULARITY SOLUTIONS FOR DIRAC-KLEIN-GORDON EQUATIONS IN ONE SPACE DIMENSION
Fang, Yung-Fu
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2004,
[23] Semiclassical states of a type of Dirac-Klein-Gordon equations with nonlinear interacting terms
Ding, Yanheng
Guo, Qi
Yu, Yuanyang
[J]. PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2023, 4 (05):
[24] ON THE REDUCTION AND SOME NEW EXACT-SOLUTIONS OF THE NON-LINEAR DIRAC AND DIRAC-KLEIN-GORDON EQUATIONS
FUSHCHICH, WI
ZHDANOV, RZ
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1988, 21 (01): : L5 - L9
[25] Semiclassical states for Dirac-Klein-Gordon system with critical growth
Ding, Yanheng
Guo, Qi
Yu, Yuanyang
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 488 (02)
[26] Bifurcation solutions for a nonlinear Dirac equation
Yu, Yuanyang
[J]. APPLIED MATHEMATICS LETTERS, 2022, 134
[27] Remarks on ill-posedness for the Dirac-Klein-Gordon system
Machihara, Shuji
Okamoto, Mamoru
[J]. DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS, 2016, 13 (03) : 179 - 190
[28] On the radius of spatial analyticity for solutions of the Dirac-Klein-Gordon equations in two space dimensions
Selberg, Sigmund
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2019, 36 (05): : 1311 - 1330
[29] GLOBAL CHARGE CLASS SOLUTIONS OF THE DIRAC-KLEIN-GORDON EQUATIONS IN ONE SPACE DIMENSION
Bournaveas, Nikolaos
Gibbeson, Dominic
[J]. DIFFERENTIAL AND INTEGRAL EQUATIONS, 2006, 19 (09) : 1001 - 1018
[30] LOW REGULARITY GLOBAL SOLUTIONS OF THE DIRAC-KLEIN-GORDON EQUATIONS IN ONE SPACE DIMENSION
Bournaveas, Nikolaos
Gibbeson, Dominic
[J]. DIFFERENTIAL AND INTEGRAL EQUATIONS, 2006, 19 (02) : 211 - 222

← 1 2 3 4 5 →