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The Generalized Saddle-Node Bifurcation of Degenerate Solution

100%

Liu P., Wang Y.-W.

Commentationes Mathematicae

2005

tom 45

nr 2

In this paper we discuss the bifurcation problem for the abstract operator equation of the form \(F (u, \lambda) = \theta\) with a parameter \(\lambda\), where \(F\colon X \times R \to Y\) is a \(C^1\) mapping, \(X, Y\) are Banach spaces. By the bounded linear generalized inverse \(A^+\) of \(A = F_u (u_0 , \lambda_0 )\), an abstract bifurcation theorem for the case \(\operatorname{dim}N (F_u (u_0 , \lambda_0 )) \geq \operatorname{codim} R(F_u (u_0 , \lambda_0 )) = 1\) has been obtained.

Exact solutions of supersymmetric Burgers equation with Bosonization procedure

81%

Ren B., Gao X.-N., Yu J., Liu P.

Open Mathematics

2015

tom 13

nr 1

Using bosonization approach, the N=1 supersymmetric Burgers (SB) system is changed to a system of coupled bosonic equations. The difficulties caused by intractable anticommuting fermionic fields can be effectively avoided with the approach. By solving the coupled bosonic equations, the traveling wave solutions of the SB system can be obtained with the mapping and deformation method. Besides, the richness of the localized excitations of the supersymmetric integrable system is discovered. In the meanwhile, the similarity reduction solutions of the SB system are also studied with the Lie point symmetries theory.

Ograniczanie wyników

1 Commentationes Mathematicae

1 Open Mathematics

2 Liu P.

1 Gao X.-N.

1 Ren B.

1 Wang Y.-W.

1 Yu J.

1 2015

1 2005

Wyniki wyszukiwania

The Generalized Saddle-Node Bifurcation of Degenerate Solution

Exact solutions of supersymmetric Burgers equation with Bosonization procedure